Lyric discussion by UWSGuy2 

Cover art for The River lyrics by Imagine Dragons

I think it's about him admitting that he's often been selfish (like in the second verse) but trying to make a change, hence the chorus: "I cleanse in the river for somebody else, for anyone but myself", meaning that he finally wants to do something for others rather than himself. Perhaps it's a symbolic cleansing, as in atoning for his selfishness, which would explain why he's doing it "for somebody else" - because others would benefit from him becoming selfless.

Yeah, that's how I hear it. Though Aider's interpretation works, it seems out of place for the tone of the lyrics overall. It's a struggle with selfishness which he can only be "cleansed" from if he does so entirely "for somebody else".