It isn't really like that, it's more abstract. It doesn't have "size" so much as it has "dimension". Try to think of the abstract concept of a line. It doesn't have an end, or a beginning, it's just a line. Now when the line "expands" it doesn't actually get bigger in any normal sense of the word, because it's already infinitely long, but things on it get farther apart. This is more like what we have with physical space, except that physical space is more complicated then a line, so the dimensions aren't all infinite (imagine more like a circle, so when it stretches out there is actually more room on the circle for things). But we're still talking about the dimensions of space, not the size of an object. It's complicated, I agree, but it's also sublimely cool to contemplate.
Yes, very cool to think about... I just think that somewhere, space has to end. I can't imagine forever. And when it does end, there has to be something beyond where it ends... =)