Critias is the name of at least two people connected with Plato’s Atlantis story, a detail that has led to some confusion and persistent debate among scholars(c). First of all there is Critias1 who actually takes part in the dialogues and relates the Atlantis story to Socrates. The Internet Encyclopedia of Philosophy has an extensive article on the historical Critias(b).
Critias2 was the grandfather of the Critias1 in the dialogues, who is supposedly one of the Thirty Tyrants who controlled Athens in 404 BC. This elder Critias conveyed the tale of Atlantis to his grandson, Critias1, who in turn told it to Socrates in the Dialogues. Critias2 was also Plato’s maternal great grandfather.