What is the importance of the title of the film? (Who is being “redeemed”, and how does he go about gaining “redemption”) ?

Redemption is right there in the title, after all. As Andy learns all too well, the system under which he is being punished is not invested in his redemption whatsoever, so he must create the circumstances for it himself. Thus, his "redemption" is a spiritual one, in that he manages to escape from wrongful imprisonment, enact revenge on his enemies, and profit enough to move to his dream home in Mexico. He goes from being trapped in Shawshank for a crime he did not commit, to finding the good life and escaping the oppressive structures that have so hurt him and his friends. Not only that, but he provides redemption and escape for his best friend from prison, Red. Red also undergoes a kind of redemption when he is let out on parole. After telling his judges that he thinks regretfully about his crime everyday, they deem him fit to leave the prison, but the ex-con's real redemption does not come until he gets the note from Andy and sets off to find a new life on the Pacific Ocean. Redemption is thus a major theme in the film, epitomized by the character of Andy and his curiously wise and generous attitude.