"Prophecy and prescience — How can they be put to the test in the face of the unanswered questions? Consider: How much is actual prediction of the "wave form" (as Muad'Dib referred to his vision-image) and how much is the prophet shaping the future to fit the prophecy? What of the harmonics inherent in the act of prophecy? Does the prophet see the future or does he see a line of weakness, a fault or cleavage that he may shatter with words or decisions as a diamond-cutter shatters his gem with a blow of a knife?"
- – Princess Irulan, Dune, "Private Reflections on Muad'Dib"
In Warhammer 40,000, a Farseer is an Eldar so far gone on the Path of the Seer that he or she cannot leave it. They are alleged to be among the most powerful psykers in the galaxy, though the job does have its drawbacks: namely, they attract the attention of Slaanesh even more so than other Eldar. As their name implies, they are primarily focused (fluff-wise, at least) on the psychic discipline Divination, though they can also use Telepathy, Telekinesis, and Sanctic Daemonology. They are also masters of advanced powers which only an Eldar Farseer can manifest, known as Runes of Fate.
For them, though, there's no time to fret about how they are trapped by their fate and beset by the hungering menace of Warp abominations—their people need their talents, so Farseers get together with other Eldar on the Path of the Seer and form Seer Councils, groups which interpret visions and act as leaders of the Eldar (in fact, they are one of the Eldar HQ choices). As the name suggests, they can see events in distant places, and even possible futures, an ability which they use to steer the Eldar in safe directions, althougth they rarely ever use it successfully. Their effectiveness is limited by their amplified Eldar pride, their refusal to share their knowledge with non-Eldar, and the apparent capriciousness of their actions to outside observers who might assume that they're simply untrustworthy nutjobs. As a result, the Farseers' plans keep getting mucked up by the other factions, and so at best, things remain at the status quo.
One of the most prominent reasons for the failures of Farseers is that they tend to forget that, as Yoda said, "Always in motion, the future is." This means that, while the Farseers might see it is possible to accomplish some goal at a particular moment in time, the situation may have already become unwinnable by the time the Eldar take action. More importantly, it blinds them to the fact that instead of choosing from existing futures, they can try and make their own future instead of agonizing about possible scenarios that may never even happen.
As Farseers grow older, their minds become so attuned with the craftworld that their bodies begin to shut down. Eventually, they leave for the Dome of the Crystal Seers at their craftworld's core, where they crystallize completely, releasing their souls into the Infinity Circuit. The discarded body then takes root, essentially becoming a statue.
Oddly (or maybe they just know we like our elf girls), every Farseer to appear in the Dawn of War games has been female but every Farseer model Games Workshop has ever released has been male. If you're looking to have a lady in charge of your Eldar tabletop army, you'd best get converting.