A blood-binder is a Shanir whose blood, if consumed by another, binds them to the blood-binder almost completely, body and soul, until death and possibly beyond. It was always rarely used; Adric explains to Kindrie in Dark of the Moon that only Highborn were bound that way, usually, and even then, only in special circumstances. Blood-bound followers were known to commit suicide when their bound Lord died.
Blood-binding is not something that has been done since the Fall, and few Shanir who had the ability have been aware of it either. Jame and Torisen are both blood-binders; Torisen's ability is revealed during what he thinks is a simulated blood-binding with Prince Odalian of Karkinaroth. "Odalian" is actually the Changer Tirandys, and the blood will be used to enable Tirandys to pretend to be Torisen after killing him. However, Torisen's blood-binder blood reacts with the Changer's blood, tearing Tirandys apart until he kills himself with the Ivory Knife.
Ashe tells Jame in Seeker's Mask that she blood-bound Bane, explaining that Bane's farewell kiss in Tai-tastigon, when he bit her lip enough to draw blood, was an attempt by him to blood-bind her, but it backfired; her blood was stronger (probably because she's pure-blood Knorth Highborn, and he's half Kendar). Instead, she blood-bound him, and this is part of the reason he still survives as a shade and is drawn to her even more so than he was in life. Ashe tells Jame that blood-binding runs in families. This does suggest that Kindrie may have the ability to blood-bind as well, given that he is pure-blood Knorth. However, since the healer is unlikely to ever try, it is possible that it will remain an unknown.
Jame warns people about the possibility when she's injured and her blood is on the ground during the tests at Tentir. This is only confirmed absolutely for her when the rathorn that has been pursuing her, intent on vengeance, licks at blood leaking from Jame's wounded wrists; he is bound by it. He fights the binding, but it is irrevocable. That Jame is a blood-binder is why Mother Ragga tells her that her blood is poison and says it again after she has bound the rathorn. She is horrified at what she has done, and begs Gorbel to kill her and set the rathorn free.
Jame uses the power of her blood against Changers in "Stranger Blood", killing one with it.
In To Ride a Rathorn, we discover that Greshan had learned to temporarily bind his younger brother, Ganth, by forcing him to ingest a single drop of Greshan's blood. The bond lasts "an hour or so", and Greshan uses the time to compel his brother to engage in unspecified acts which involve Ganth's nudity. This is the source of Ganth's pathological aversion to Shanir powers.