Ping has been well explained above. I won't say more.
Just an advice for server choice:
Ping higher than 300
you can't play anything but chess and turn based strategy games.
Ping between 300 and 150
It depends on the game you are playing: battlefield 1942 will be choppy but playable, serious sam 2 will be still enjoyable (no precision fire needed), Medals of honor will be really difficult to play since it requires aiming skills and fast reflexes.
Ping under 150
Do whatever you want and kick some serious youknowwhat
Also mind that some servers have ping autokick: this means that if your ping (instant or average) goes beyond the specified value, you will be kicked. Usually this is specified in the server name, so don't bother joining a server with autokick 150 (most MOHAA servers)if your ping is 300.
One last thing: the in game ping might be actually slightly higher or lower than that you can see on gamespy arcade window, so beware if your ping is 149...