George is Ann's brother and he functions in the play's second act as an inquisitor and antagonist to Chris and especially to Joe.
George does not believe Joe Keller's story about what happened in the factory to lead to the sale of the faulty airplane parts. George has spoken to his father, in prison, and heard a version of the story that does not match with Joe's story.
After visiting his father in jail, he confronts Joe. George is convinced that Joe destroyed his father and was the real instigator of the crime.
George challenges Chris's plan to marry Ann and charges her with siding with the family that ruined her own family.
George presses Joe to admit the truth about his role in that sale, but Joe resists and continues to deny his responsibility in the matter, saying he was sick that day.
George can be seen as symbolizing the repression of the truth, the righteousness of the falsely accused/victim, and the break between the Keller's and their past.
George was once a close friend of the family and a neighbor. Now he is angry and brings a serious accusation against Joe Keller (and, by implication, his wife too).
George is the brother of Ann and the reason that he is important is because he causes and brings a lot of conflict when he is invited to come stay at the keller's house. He also helps the audience/reader learn more of Ann's backround.