What is ping that I see in my games?

Here is Wikipedia's definition.

The tl;dr version is that ping is the time that it takes for a network packet to leave your computer, go to the game server, then return back to your computer. Lower=better. Ping is usually measured in milliseconds. So for example, in a FPS (First Person Shooter) game, if you had a 500 ping, everything you see on the game is on a .5 seconds lag. If you were to snipe someone, you would want to aim for where they would be in .5 seconds.