I'm not very bright, so can someone here explain in simple layman's terms exactly what the universe is expanding in to.
Your question presumes something outside of observable space-time. We have no way of answering that question, if it is indeed a coherent question, in a way that “what happened before the beginning” is not.
All we can say is that observable space-time has been occupying an increasingly greater volume. That fact does not require another larger, non-space to contain it, nor could we speak meaningfully about it in any scientific sense, since our physical laws could not be presumed operative outside our own observed universe.
That's a very bright question. The answer is that the universe isn't expanding into anything. There is nothing but God outside the universe. Not even space or time.