Ping is the number of milliseconds it takes for another machine (usually the server) to receive a response from yours on a network packet. A lower ping means that your machine responds faster to the server, and hence your position and status is updated more often.
A high ping means that your connection is slow, and you are updated less often, which often leads to problems like lag or players warping past you, etc.
In multiplayer online video games, ping refers to the network latency between a player's computer (client), and either the game server or another client (i.e. peer). This could be reported quantitatively as an average time in milliseconds, or qualitatively as low ping or high ping. The latter usage is common among players of first-person shooter and real-time strategy games. Having a low ping is always desirable because lower latency provides smoother gameplay by allowing faster updates of game data.