Braids is a psychopath, or dementia summoner, working for an evil crime syndicate known as the Cabal. She's very powerful, even one of the right-hand-persons for the Cabal leader, known as The First (or the Patriarch). Her card is pretty cool, forcing everyone (even her controller) to sacrifice cards. Evil black mages love using her card. She was a major part of the storyline, having served The First, captured Jeska so she could become Phage, eventually killing The First, and all-around acting like a raving lunatic. A lot of good quotes come from her, as well. Sadly, this awesome character was killed off rather matter-of-factly by Akroma, a total pile of crap, and an even crappier card.
As for what dementia mages are. Well, the nightmare cards in Torment protray the powers of dementia summoning. Supposedly, mages of the Cabal are able to go into "dementia space" and bring out nightmarish versions of anything they have ever killed. Thus, they kill something, use the nightmare version to kill something bigger, and keep going like that until they have a whole arsenal of nightmare creatures to use. Chainer, a legend and character from Torment, depicts a normal dementia summoner, though in the storyline he had the power of the Mirari and was actually better at dementia magic than normal mages.