Gravity is often made more complicated than it should be explained.
You can see in the GIF above that the big stationary object in the middle is sat on spacetime and it curves that spacetime towards it. You can also see that a different moving object supposed to represent a planet or whatever is moving around it and also warps the spacetime, which then warps back after it has passed.
Gravity is just the name given to that bending of spacetime. It isn't anything else, it's just the name for that curve.
You might here things like "no light can escape because the gravity of a black hole is too overpowering" or something like "light bends around stars" and stuff of this nature. Once you understand that gravity is a bad name for curvature (or you can even say that gravity is another name for acceleration, because you're measuring the effects of that curvature), these things become pretty simple:
In Figure A the curving of spacetime due to an object (that isn't shown, pretend a Sun is there) distorts the red light beam and makes the circle think it's coming from somewhere else. Because spacetime is curved and light travels across spacetime then it can't just "jump", it has to follow the curve.
In Figure B is a black hole showing why a very large distortion of spacetime like a blackhole means that light can't escape. It goes so far down that it doesn't have the energy to get up the other side of the hill, so to speak.
Now remember that we live in a 2D world and not a 3D world, so when we see the above we're actually talking about a 3 dimensional grid/mesh that is being warped:
So we don't float away into space because all of the space around us in 3D is curved by the mass of the Earth. We have to insert energy into us to "get up the hill" of the curve so to speak which is why flying and space travel is so very difficult and requires big engines.
Now that you understand what gravity
is, ask yourself this question. If gravity warps spacetime and things move through spacetime then shouldn't that movement create a ripple of some sort?
Einstein said yes. Some other people said no. Einstein was right.
The ripple however is so small and hard to detect because it doesn't really affect the matter within spacetime. Why doesn't the ripple created when you spit over the side of a cruise liner tip the whole ship over? Because it's incredibly small compared the distortions of the whole ship has on the water and the ship is sat on the water itself.
This is exciting to many scientists because
everything in the Universe moves. What we think of as temperature is in another way of looking at it just how fast things move. Anything that is above absolute zero has some form of movement to it and will generate gravitational waves which can be detected and we can find information about it. That is science fiction at the moment because we've only just been able to detect the movement of black holes which are massive and make massive waves comparatively (but still not big enough to be noticed by the ship) so detecting gravitational waves from atoms seems like an impossible task but it opens up a whole new branch of science.
The first telescopes used visible light to look at things. Then we got smarter and used non visible light and radio waves aswell. Now we've got a bit smarter than that even and can now use gravitational waves to look at things. This is especially important for early age cosmology as unlike electromagnetic radiation which has a time limit on it, gravitational waves could theoretically look right back to the Big Bang itself. Just as on a perfectly calm ocean a stone's ripple from one side would reach 1000 miles away, the ripples in spacetime don't go anywhere and are still available to be measured.