Ping is the measurement of time taken for information to travel from one point to another over a network. E.g. Speed of information traveling from your computer to a game server. A 'ping' estimates a round trip time using interval timing responses and will generally give you a result that's measured in 'milliseconds'. A likely scenario for a Dial up connection 'ping' time to a Broadband connection 'ping' time could be 400ms and 40ms respectively.
To give you and example of how this might work in an online situation would be to imagine that you are playing a 'shooter' game against other players online. On you're screen you have a weapon of some description that you shoot at your opponent. He too, also has a weapon and is shooting toward you at almost the same time but a split second later than you. However, you are on a Dial up connection with a very high ping and he is on Broadband with a low ping. A likely virtual interpretation would be that you get shot by him first but he doesn't get shot by you at all even though you shot first. Why? This is because the information sent from his client (computer) to the game server was faster (lower ping response time) and reached it before your information reached the game server. So you see, if you’re playing a game of cards when there is quite sometime in between turns, ping doesn't really matter. But in other games, it can be quite influential on the outcome.