The length of time, in milliseconds (thousandths of a second) that it takes for a basic message to travel from your computer to another computer and back again (round trip time).
It's not very important for most things like general surfing, as you are unlikely to notice the difference between a 500ms and a 50ms ping in the time it takes a page to load, but it is critical if you do any form of online gaming as it is a measure of the game's responsiveness to your pulling the trigger etc.
The name comes from the noises that boats and subs make when using sonar. As seen in any stereotypical post-WWII navy film, that suspense filled period when the sub's crew all go quiet as the seeker passes directly over their heads and all you can hear is the "ping" of the sonar...