Well, our universe does have an edge — that is, if by "our universe," you mean the observable universe. The speed of light is just that — a speed — and the universe has only been around for so long (about 13.77 billion years), which means only so much of the universe has been revealed to us via the light that has traveled those vast cosmic distances. And what's outside our observable limit? That one's easy: It's just
more stuff, like galaxies and black holes and new, fantastic varieties of cheese. It's forever unreachable by us, sure — but it's still over there.
Where's the Edge of the Universe?