You can think of this space as something that tells for every point a path passes through, how long the distance of the path in that point is. So when I connect

You can think of this space as something that tells for every point a path passes through, how long the distance of the path in that point is. So when I connect A and B with a path, and I take the integral of space on that path, I get the length of the path I would travel if I go from A to B along this path. One step further, the distance from A to B is the shortest length of all paths from A to B. Now if for every point in the universe, we have those numbers for each path through that point, we call that a "metric". Einsteins laws tell us how those numbers all relate to each other and how changing the numbers at one point affects the numbers at other points over time. And from those laws, you can see that you can have waves within those numbers. So it is not "something" that is waving, it is space itself, the thing that defines distances, the metric, that is waving. Now the annoying thing is that that means that two points at rest with each other, can be at a changing distances from each other. What happened is that the space between them was waving, changing which path between the points was the shortest path, and how long that path was.