You can find articles about how doing good things (like helping other people, species, etc.) are rewarded in the brain, in the same area it rewards us for eating food and having sex. So, generally, morally good deeds feel nice. Mix it with the 9999 other aspects of the human brain and you get people passionate about destroying injustice and all that jazz.

I agree that we're just a spec of a spec in the Universe and that everything is pretty much pointless, but hey, I'm not going to be an ass because of it.