The story of Jake LaMotta, a boxer with more rage than Mike Tyson ever had, is hard to describe. He was a great boxer, a tragic figure, and a fascinating character. He was proof that human beings are, despite millions of years of evolution, despite all our culture, education, and pretenses to the contrary, animals. Jake LaMotta's rage and extreme behavior showed how ugly and beautiful we all can be, and his story remains haunting. That his hard life became the basis for this film is probably its most redemptive quality. And it gave Robert DeNiro the role of his lifetime.
You should read this fascinating article about how this movie came to be made. It not only redeemed LaMotta but also Scorsese, showing that no one is beyond redemption.