I have a great thought experiment that I love to use in order to illustrate this point.
You know those old Arcade games where if you go passed one side of the screen, you loop around and come back out the other? Like in Pac-Man or Joust. Sometimes, falling down brings you back up to the top of the screen, too.
So imagine being in a cube composed of mirrors on the inside. You can hold a light in order to actually see inside of the cube. Everywhere you look, up, down, left, right, you're repeated infinitely based on how large the inside of the cube is.
Here's where it becomes a universe. Take this same observation, but remove the cube itself, leaving you and all of your infinite reflections to fall. Wherever the glass was before, you now "wrap around" back to the top of the cube in the reflection underneath you.
At this point, there's no longer any way to tell where the "edge" of the cube would have been, because the glass is gone and the only other thing that exists in this space is you. You can only tell how far away you are from yourself, thus having a rough estimate of how large the space is.
So let's imagine that, all around you, the space between your reflections starts increasing, as if the walls and ceiling of the original cube had begun to expand. Except, within the cube, it's not expanding "into" anything. The space is just getting stretched further apart.
That's kind of like what we're seeing on a cosmic scale. The difference is that there might not even be an "outside" to our space, like there would be for this non-euclidean cube: space itself exists self-continuously within itself. For all we know, all there is are the reflections, but we don't know how far we would have to travel in order to end up where we started again and thus we don't know how "big" the universe is for sure.
Many models seem to suggest that it used to be much smaller than depicted in this thought experiment, but it's been rapidly expanding over billions of years. We can tell, in part, because the gaps between things are growing.