Elmo Blatch was a robber who killed Andy Dufresne's wife and her lover.
Despite appearing only briefly, he plays an extremely important role in the story. He is the real killer of Andy Dufresne's wife and lover, which is the crime Andy was imprisoned for. Due to the fact that Andy does not bother to clear his name after his escape from Shawshank Prison, and Norton killed Tommy to keep him quiet about Andy being innocent, Blatch presumably got away with the crime.
Blatch is a braggart and an egomaniac whose exaggerated accounts of his exploits fool none of his listeners into believing that he is the master criminal whom he makes himself out to be and is the prisoner no one wants to share a cell with.