I know the galaxies are moving away from us (faster and faster) but when we say the universe is expanding, is that really only pertaining to the galaxies expanding or is the space itself expanding? I know we don't yet know what the boundary is, but I just wanted clarification around the commonly used phrase "Universe Expansion".
Yes, the idea is that the universe actually is expanding -- the "fabric of space" if you will. The common analogy is to think of baking a loaf of raisin bread where the batter is the universe and the raisins are galaxies. As the bread expands while baking, the actual universe is getting larger, and the galaxies are just getting carried along for the ride.
Another common analogy if you want to picture the universe as two dimensions expanding into three (because we think the universe is three dimensions but warped in higher dimensions) is to think of a balloon. Take the balloon, uninflated, and draw dots on it (those are your galaxies). Now blow the balloon up. The surface of the balloon is the universe, and it's the universe that's expanding while the dots (your galaxies) are moving away from each other because of it.
That's really the basic story in a nutshell, though I know it can be hard to understand since we think of the universe as being empty, so how can emptiness expand? There is actually a pretty good Wikipedia article on the expansion of space that has some nice conceptual diagrams illustrating how this works, and the best part -- no equations! :-)