A Seer Council is a collection of Eldar who walk the Path of the Seer, Eldar who have developed their psychic abilities. Seer Councils serve to train those who have decided to walk the Path, which is the most treacherous of the Paths, as an untrained psyker is a magnet for Daemons. A Seer Council consists of between two and five Farseers and at least three Warlocks but not restricting the total number. Due to this, the majority of them are armed with either a Witch Blade or a Singing Spear.
Besides training Eldar on the Path of the Seer, a Seer Council will usually serve as the governing body of a Craftworld (with Craftworld Biel-tan and Craftworld Saim-Hann being notable exceptions). They will take visions Seers have received and try to interpret them as best as possible. The amount of times this ends up backfiring on the Eldar varies from vision to vision but can be guaranteed when it does to result in lolz.
Seer Councils at times have been noted to have an alarming tendency to be slaughtered en masse, perhaps the universe teaching them a lesson for being such dicks or Tzeentch doing some trolling. That, and the fact that their 'visions' often come to bite them back in the ass, one must wonder how anyone takes them seriously. If it wasn't for Eldrad literally carrying the entire team, then the entire Asuryani would have crashed their Craftworlds in the Eye of Terror due to their incompetence.
On the tabletop they are a mixture of Farseers and Warlocks although in Dawn of War they were all warlocks, perhaps because having a squad of Farseers in the game would have been too overpowered even for them. They all wear Rune Armour which makes them a bit more survivable in a fight, although the fluff seems to ignore that.