The metric expansion of space is one of those things you just have to kinda accept, it's too far outside our normal experience of life otherwise.
My favourite part about it is that as
@Shakesy says, it happens everywhere at the same time. Very, very, very, very slowly, but the Universe is so stupidly big that it adds up, and the further apart things are the more space has been created between them. And at some point in the near future, astronomically speaking, our Observable Universe is going to be as big as it's ever going to get, as the distance between us and anything outside of it is increasing by more than the speed of light (technically it is still going to grow for a while even then, but by and large that's true).
Eventually even the things inside of it are going to start fading from view as the light from them redshifts out of our ability to detect them. If we take that far enough, we'll eventually reach a point where anything that isn't our galaxy (at that point a merger of our galactic backyard the Local Group) will have faded from view and be undetectable. Ultimately, any intelligent life that arises in that galaxy will conclude that the Universe is static and eternal, and concepts like the Big Bang and the evolution of the Universe will be unknowable.
Fun times.