You seem to be REALLY confused about things, so i'll try to break it down for you.
A mesh is just a collection of points/triangles in space. It's used interchangably with the term model and usualy means the same thing.
You don't get access to individual pixels on the screen itself, what you can do is access them before they're put on the screen, if that makes sense. OpenGL allows rendering to a, so called, frame buffer, it's like rendering to an image in memory, this allows you to apply post processing effects. I don't know how libgdx does it though.
Now there are plenty of ways to do ripples and it depends on what kind of an effect you're looking for, though you haven't specified anything. You could just do a ripple animation and blend it with whatever picture you have, you don't need OpenGL for that. Other than that you could put your finished image through OpenGL and let it apply ripples as some sort of a displacement based on a normal map. There's plenty of articles that cover this subject. The issue is that if you don't understand how OpenGL works, then none of this is going to help you, really.