It is space itself that is expanding, not some void that lies beyond the edge of the universe.

Imagine a balloon that is covered with cotton balls that have been glued to it. Those cotton balls are galaxies, and the rubber of the balloon is space. Now, blow up the balloon - the cotton balls will get farther apart from each-other, but won't be expanding into anything (after all, the balloon is round - if you walked around it far enough, you would return to the same spot).

The universe is kind of something like that: space is getting bigger, and as a result the distances between galaxies are increasing, but there is no outside of the universe that matter is moving into.

How big is the universe? We don't know. We can see a distance of about 13.7 billion light years, because the universe is 13.7 billion years old and light only travels so fast. As the universe gets older, we can see farther, because light has had more time to travel. There is no indication that there is an edge of the universe of any kind in any direction. The universe may be infinite in size, and yet is still expanding despite being already infinite.