There's no campaign mode per se, but you can play it solo. The story is also very barebones, it's really just meant to carry you into these levels. It's very sci-fi space opera-esque, something about the future and an evil army, and you're these warrior/machines from a time long past brought back to help free people or something. Some guy just mentioned something about some evil sisters running the show... I don't know.
But yeah, it's all about getting into these co-op levels with your friends and just having fun. Think Diablo with an Unreal Tournament aesthetic.