Answer:
I guess really, it doesn't!
The big bang theory in itself is filled with flaws and obscene estimations.
I really can't think of any scientific explanations out at the moment that truly explain it...
Sure, the big bang theory tells us that a singularity- a huge amount of pressure building up in a incalculably small speck eventually exploded, and caused reactions that created planets, stars and eventually, us.
However, scientists just can't answer where that singularity came from- or how it was created. Some believe that a 'big crunch' will happen in the next few billion years- where effectively, the universe gets sucked back into that singularity, and so we have a constant circle of crunch- singularity- bang- life- crunch. A never ending cycle.
But again, this doesn't explain how it all began. It can't have just been happening, without a beginning- unless you remove time- but that doesn't happen.
Basically, the only thing that I know of that explains the origins of the universe is the Christian/Jewish account of creation by intelligent design.