Commonly practiced by
sambo,
jiu-jitsu and
judo students,
grappling is simply ground-fighting -- truly effective against only one opponent, of course.
Similar to wrestling, grappling well requires a very detailed understanding of body mechanics, incredible stamina and excellent balance.
When grappling, each opponent tries to induce the other to submit -- usually by applying a choke or joint manipulation. In tournaments, matches are usually three minutes in length (although note that in one of the most prominent no-holds-barred tournaments in which grappling played a major role, the first Ultimate Fighting Championship, Royce Gracie beat Dan Severn in a match that lasted almost 16 minutes).
The guard (one person lying on their back with their opponent between their legs) is probably the most common position to find yourself in when grappling -- one of the first things to learn is how to pass it.
Proponents for grappling argue that nearly every street fight eventually goes to the ground, and that because of this, anyone interested in being able to defend themselves should be good on the ground. Opponents (those that prefer stand-up fighting like tae kwan do or kickboxing) will counter that grappling is only good against one opponent, and regardless, fights don't *have* to go do the ground if you're good on your feet.