The major points (spoilered not for spoilers, but for length):
(Not-so) brief overview:
Spoiler
The armies of the Light all agree to join Rand's forces at the Field of Merrilor, but only if the Seanchan agree as well. They do. The armies of the Light engage the Shadow on four fronts: at Caemlyn, in south-eastern Kandor, at Tarwin's Gap and at Shayol Ghul itself. Elayne commands the Caemlyn front and wins a great victory, utterly destroying the Trolloc army that burned Caemlyn after a gruelling running battle through Braem Wood and to the walls of Cairhien. The Tarwin's Gap front is bravely held, but ultimately overwhelmed. Lan retreats, burning most of Shienar as he goes, falling back on the Field of Merrilor. The Kandor front is very successfully held until Demandred arrives with an army of several hundred thousand Sharans (from the eastern lands beyond the Aiel Waste) and 400 Ayyad. In a surprise attack he almost annihilates the Aes Sedai, wiping out two-thirds of them and half their army. They are forced to fall back on Merrilor.
The Seanchan join the allies at Merrilor, but it becomes clear that the major generals (Agelmar, Gareth Bryne, Davram Bashere and Rodel Ituralde) have been compromised, Compelled by Graendal from Tel'aran'rhiod to become incompetent. Mat takes over (there's no other choice, especially since his medallion renders him immune to Graendal's corruption). He organises a massive, last-ditch defence of Merrilor which allows the Light to destroy many hundreds of thousands of Trollocs with relatively few losses. Demandred soon proves to be a popular target. He kills Gawyn in single combat, almost kills Galad in single combat (Annoura saves him and gets him back to Mayene - the Light's hospital - for Healing at the cost of burning herself out) and defeats Logain in a Power duel.
The Darkfriend Asha'man are defeated in the Black Tower, with Logain and his loyalists defeating Mazrim Taim. Taim and his loyal forces join the Shadow and Taim is made a new Chosen, M'Hael. Using an ultra-powerful sa'angreal to weave balefire on a colossal scale, threatening to unravel the Pattern, Taim almost wipes out the remaining Aes Sedai. Egwene faces him down and uses a new superweave called the Flame of Tar Valon to check balefire. It's an anti-balefire which regenerates the Pattern. She restores the Pattern and kills Taim, but can only match his sa'angreal by channelling more of the One Power than she can safely use. She kills herself in a massive eruption of the Power rather than face a life as a stilled channeller. This eruption kills the remaining Ayyad and gives Rand (locked in metaphysical combat with the Dark One at this point) a clue on how to save the day.
Lan comes into possession of the foxhead medallion and uses it to charge Demandred. Lan uses his powers as a Taciturn Badass to kill Demandred. Ironically, he uses that 'sheathing the sword' thing (let someone stab you so you can kill them) to kill Demandred in the face. The Shadow is dismayed but could still win due to overwhelming superiority of numbers. However, Faile and Olver have been escorting the Horn of Valere to Mat. After some detours, they reach the battlefield and, thanks to Bela (I'm not even joking) evade Shadowspawn long enough for Olver to blow the Horn: it turns out that Mat was severed from it when he was killed and the saved (by balefire) back in Book 5. The Heroes of the Horn show up to kick some backside on a colossal scale, though not by themselves (this isn't Minas Tirith and the Army of the Dead; the Heroes can be killed, it transpires, and they need the other troops to back them up). The good guys win at Merrilor. Moghedien survives the battle and tries to sneak off the field, but is imprisoned by an over-eager Seanchan sul'dam (although technically they are not supposed to be taking damane via their treaty with Rand and Egwene, but they decide to keep Moghedien).
Perrin spends all of this time stalking Slayer through the wolf dream. He finally gains Slayer's mastery over the wolf dream and kills him at Shayol Ghul. He is almost Compelled by Lanfear into helping her kill Rand, but his mastery of Tel'aran'rhiod allows him to resist her Compulsion and to snap her neck, killing her for good. When the Horn is blown, a whole army of spectral wolves show up to fight alongside Perrin against the Wild Hunt (a massive influx of Darkhounds). Graendal stalks the battlefield and is responsible for many deaths (including Rhuarc's) before Aviendha engages her in battle. She nearly kills Aviendha, but Aviendha uses her 'exploding gateway' trick to take Graendal out. Graendal actually survives, but her Compulsion reverses itself into her, turning her into a drooling idiot. Just when you think it's all over, Padan Fain/Mordeth/Mashadar shows up and starts killing everyone, but it transpires that Mat is immune to his powers thanks to his long exposure to the dagger. Mat simply stabs Fain in the heart with the Shadar Logoth dagger.
Through all of this Rand and the Dark One engage in a metaphysical philosophy-off in Shayol Ghul that literally lasts for 500 pages (not continuously, being intercut with roughly 100 other POVs spanning four massive battles). During this philosophy-off we discover that the Dark One's existence as a force of chaos is what gives humanity its competitive edge and its will to survive. When Rand plans to kill the Dark One and remove him altogether, the Pattern (not the Dark One) shows him what would happen instead: people who no real spark or invention to them, living like zombie hippies. Rand decides to re-imprison the Dark One again. How he does this without making the same mistakes as Lews Therin is to set up a feedback loop. He tricks Moridin into picking up Callandor, which acts as a sa'angreal for the True Power. Moridin doesn't know about the flaw that allows women to take control of the person using it, so Moiraine and Nynaeve seize control of him through it. Rand then wraps saidin (from himself) and saidar (from the two women) in the True Power, protecting them from the Dark One's taint, and channels it into the Dark One, effectively holding the Dark One completely imprisoned. At the appropriate signal, the Seals (held by Logain at this point) are shattered, smashing open the Dark One's prison. Rand uses the combination of the One Power and True Power to regenerate the Dark One's prison from scratch, with no Bore, Seals or patch. The Dark One is locked back away.
Rand has pretty much been drained of life by all of this. However, thanks to his balefire bond with Moridin, he is able to undertake a soul-swap. Moridin, in Rand's body, dies and is burned with everyone thinking it's Rand. Rand wakes up in Moridin's body and decides to go walkabout. He can no longer channel, but has a saa the shape of the Dragon's Fang in his eye. He can apparently warp reality, however, at one point summoning a flame without channelling. He heads off to see the world. Only Min, Aviendha and Elayne know the truth, but Cadsuane and Nynaeve suspect (I wouldn't be surprised if Moiraine does as well).
The Seanchan join the allies at Merrilor, but it becomes clear that the major generals (Agelmar, Gareth Bryne, Davram Bashere and Rodel Ituralde) have been compromised, Compelled by Graendal from Tel'aran'rhiod to become incompetent. Mat takes over (there's no other choice, especially since his medallion renders him immune to Graendal's corruption). He organises a massive, last-ditch defence of Merrilor which allows the Light to destroy many hundreds of thousands of Trollocs with relatively few losses. Demandred soon proves to be a popular target. He kills Gawyn in single combat, almost kills Galad in single combat (Annoura saves him and gets him back to Mayene - the Light's hospital - for Healing at the cost of burning herself out) and defeats Logain in a Power duel.
The Darkfriend Asha'man are defeated in the Black Tower, with Logain and his loyalists defeating Mazrim Taim. Taim and his loyal forces join the Shadow and Taim is made a new Chosen, M'Hael. Using an ultra-powerful sa'angreal to weave balefire on a colossal scale, threatening to unravel the Pattern, Taim almost wipes out the remaining Aes Sedai. Egwene faces him down and uses a new superweave called the Flame of Tar Valon to check balefire. It's an anti-balefire which regenerates the Pattern. She restores the Pattern and kills Taim, but can only match his sa'angreal by channelling more of the One Power than she can safely use. She kills herself in a massive eruption of the Power rather than face a life as a stilled channeller. This eruption kills the remaining Ayyad and gives Rand (locked in metaphysical combat with the Dark One at this point) a clue on how to save the day.
Lan comes into possession of the foxhead medallion and uses it to charge Demandred. Lan uses his powers as a Taciturn Badass to kill Demandred. Ironically, he uses that 'sheathing the sword' thing (let someone stab you so you can kill them) to kill Demandred in the face. The Shadow is dismayed but could still win due to overwhelming superiority of numbers. However, Faile and Olver have been escorting the Horn of Valere to Mat. After some detours, they reach the battlefield and, thanks to Bela (I'm not even joking) evade Shadowspawn long enough for Olver to blow the Horn: it turns out that Mat was severed from it when he was killed and the saved (by balefire) back in Book 5. The Heroes of the Horn show up to kick some backside on a colossal scale, though not by themselves (this isn't Minas Tirith and the Army of the Dead; the Heroes can be killed, it transpires, and they need the other troops to back them up). The good guys win at Merrilor. Moghedien survives the battle and tries to sneak off the field, but is imprisoned by an over-eager Seanchan sul'dam (although technically they are not supposed to be taking damane via their treaty with Rand and Egwene, but they decide to keep Moghedien).
Perrin spends all of this time stalking Slayer through the wolf dream. He finally gains Slayer's mastery over the wolf dream and kills him at Shayol Ghul. He is almost Compelled by Lanfear into helping her kill Rand, but his mastery of Tel'aran'rhiod allows him to resist her Compulsion and to snap her neck, killing her for good. When the Horn is blown, a whole army of spectral wolves show up to fight alongside Perrin against the Wild Hunt (a massive influx of Darkhounds). Graendal stalks the battlefield and is responsible for many deaths (including Rhuarc's) before Aviendha engages her in battle. She nearly kills Aviendha, but Aviendha uses her 'exploding gateway' trick to take Graendal out. Graendal actually survives, but her Compulsion reverses itself into her, turning her into a drooling idiot. Just when you think it's all over, Padan Fain/Mordeth/Mashadar shows up and starts killing everyone, but it transpires that Mat is immune to his powers thanks to his long exposure to the dagger. Mat simply stabs Fain in the heart with the Shadar Logoth dagger.
Through all of this Rand and the Dark One engage in a metaphysical philosophy-off in Shayol Ghul that literally lasts for 500 pages (not continuously, being intercut with roughly 100 other POVs spanning four massive battles). During this philosophy-off we discover that the Dark One's existence as a force of chaos is what gives humanity its competitive edge and its will to survive. When Rand plans to kill the Dark One and remove him altogether, the Pattern (not the Dark One) shows him what would happen instead: people who no real spark or invention to them, living like zombie hippies. Rand decides to re-imprison the Dark One again. How he does this without making the same mistakes as Lews Therin is to set up a feedback loop. He tricks Moridin into picking up Callandor, which acts as a sa'angreal for the True Power. Moridin doesn't know about the flaw that allows women to take control of the person using it, so Moiraine and Nynaeve seize control of him through it. Rand then wraps saidin (from himself) and saidar (from the two women) in the True Power, protecting them from the Dark One's taint, and channels it into the Dark One, effectively holding the Dark One completely imprisoned. At the appropriate signal, the Seals (held by Logain at this point) are shattered, smashing open the Dark One's prison. Rand uses the combination of the One Power and True Power to regenerate the Dark One's prison from scratch, with no Bore, Seals or patch. The Dark One is locked back away.
Rand has pretty much been drained of life by all of this. However, thanks to his balefire bond with Moridin, he is able to undertake a soul-swap. Moridin, in Rand's body, dies and is burned with everyone thinking it's Rand. Rand wakes up in Moridin's body and decides to go walkabout. He can no longer channel, but has a saa the shape of the Dragon's Fang in his eye. He can apparently warp reality, however, at one point summoning a flame without channelling. He heads off to see the world. Only Min, Aviendha and Elayne know the truth, but Cadsuane and Nynaeve suspect (I wouldn't be surprised if Moiraine does as well).