What is the universe expanding into? Well that's a good, yet slightly mislead question. Often when we learn about the expansion of the universe we are told to envision it as a balloon that’s being blown up. Dots on the balloon represent galaxies, and as the balloon is blown up, the space between galaxies increases, representing the expansion of the universe. This is a somewhat poor analogy, as it makes us think of the universe as an object that expands into a surround space (the air in the room). This is not true. Instead of thinking about the universe as an object that expands into another space, think about it as a sheet of rubber. The universe contains any imaginable space, and can be stretched like a rubber band. Don't think of universe expansion as galaxies hurtling outwards pushing the edges of the universe farther and farther out. Imagine instead that the galaxies are stationary, and that the space between them is stretching, causing the universe to expand.
This helps answer the question: what is the universe expanding into? Well, since the universe is all space, it's not expanding into anything. Rather, the entire universe is stretching and becoming larger.
It's ok if your still a bit confused…. So are astronomers! There are various theories about the structure of the universe and how it moves. Until we can come up with some observational evidence proving one of these theories correct, we will all sit here puzzled about the "edge of the universe" and what might be "beyond" it.