One of the biggest goals in each one of our lives is to figure out our purpose. Why do we exist? Not how ... because the answer to that is known, but why? Explanations involving God just result in the question being modified to: Why does God exist? Now, I recognize that I am making an assumption here (which, if proven false, would render this entire chain of thought invalid), justified by the lack of convincing evidence to the contrary, but this is what I fundamentally believe as of now: there is no greater purpose.
The universe, as a result of the fact that it is logically consistent, can exist. But so can any number of other logically consistent universes with different histories or different laws of physics altogether. And why should anything exist at all anyway? Well, the principles of justice that I have been conditioned to think according to (yes, I know that it sounds evil, but if you think about it objectively, the definition does apply) make me want to believe that all possibilities are (withholding the word: equally) feasible, and exist as a superimposition which happens to be most closely described by the term: Multiverse. But essentially, we exist, because we can.