Ok this is probably dumb, but can someone explain a flat universe to me?

[no limit]

I was never good at math in school, but physics has been really fascinating me lately. I keep hearing the universe is flat which makes sense to me, if you shoot a really powerful laser out in to space it will remain flat. But what I don't understamd is how gravity plays into this. When I think of gravity I think of the following picture which was always taught to me:



What I don't get is the satellite. If gravity attracts objects in a flat matter as that picture above suggests how can the satellite be above the earth? And how can there be up/down? It would seem that everything would have to be flat. When you look at the stars at night no matter where on the planet you are the stars are everywhere, up, down, left, right. But gravity seems to paint a flat picture which would make that impossible. Is there anyone out there that could explain gravity to me in layman's terms?