I love this question. The way I've heard it explained is that the universe has eternally been in a state of flux. The Big Bang occurred when all the matter of the universe condensed into one infinitely dense dot of material that fused and exploded violently. The resulting expansion is what we live during now. After a few more billion or possibly more years, the expansion will slow and stop, and gravity will slowly draw all the matter of the universe back again to a central point, where it will all begin again.
As to where all the matter originated is a matter of speculation, unless you're the God-fearing sort.