Thesus and Pirithous were good friends, good adventures, and rather stupid. Deciding that they needed an adventure, they captured Helen (later to be Helen of Troy) the most beautiful child (she's twelve at the time) in the world. They drew straws for her, promising that whoever lost would be helped by the other to gain the wife of his choosing. Thesus won Helen, and while waiting for her to mature, decided to pursue Pirithous’s dream girl. (After they left Helen was rescued by her brothers Castor and Pollux, who seized Athens, also twelve at the time)
Pirithous wasn’t real bright, though. He decided that he wanted no other wife than Persephone, the most guarded woman ever. He justified that he could take her even though she was already married by that she didn’t love her husband. (and he though, "hey, I’ll just explain this to Hades and he’ll be quite happy to let me take her." Did this guy have any brains at all?)
So, they proceeded to the underworld, told Hades this, and, with his usual civility, Hades told them to sit down so that they could talk about it. They were quickly trapped on their chairs, and though eventually Theseus was freed by Hercules, Pirithous became a permanent resident. In some cases, the stones close about them. Usually the chair is refered to as the Chair (or Seat) of Forgetfulness.