When you plug/cover/pinch one nostril closed and then blow hard to make unwanted snot shoot out the other nostril. Sometimes when suffering from a cold, snot rockets can be achieved by the nose alone, without intervention from the hands. The primary purpose of the "rocket" is to avoid leaving any snot residue left behind. The idea is to blow the snot out fast enough so that it has no chance of sticking to the end of your nostril. Snot rockets are enacted primarily in situations when tissue is desperately needed but unavailable, or it is done simply for recreation.
My nose was starting to run before the track meet, so I ran behind a tree and blew out a massive snot rocket.
Snot rockets are about the only fun part of having a cold. Morning snot rockets in the shower are cherished by many.