You weren't the only one wondering that; the ending perplexed many. But the film's director Scott Cooper explained it in interviews, like this one. Here's the gist:
After being thwarted by law enforcement officials, Russell kills Harlan DeGroat (Woody Harrelson), the meth-addicted crime boss responsible for murdering his brother, right in front of the local sheriff (Forest Whitaker). Cooper then cuts to Russell sitting quietly in a living room, before fading to black. "It's an homage to 'The Godfather Part II,'" Cooper said, referring to the final shot of Francis Ford Coppola's 1974 Best Picture winner.
"This is a man who is battling his soul and living with the consequences of violence. When he went to kill Harlan DeGroat, he thought he could have gone to prison or be killed by the police. He never thought he would get off and that the sheriff would ultimately say, 'Let me make this right.' And he does," Cooper said of the finale of his film, which takes place at an undated point after Russell has murdered DeGroat. "This is a man who, whether he is [in] prison or not, he's in prison for the rest of his life. Hopefully he will find peace and contentment at some point. I'm a very optimistic person, I hope that, ultimately, Russell Baze does find that."
So the ending simply shows us how Russell, like Michael Corleone in The Godfather Part II, will have to live with what he did (and reflect on it) for the rest of his life.