To fire an explosive missile at your feet whilst jumping, the act of which makes you accelerate quickly upwards. You must jump whilst doing this, because otherwise you will not gain much speed upwards and will inflict a lot more damage on yourself. Timing is important.
A mechanic in Team Fortress 2 that allows the soldier class to maneuver great distances at a high speed by shooting rockets at surfaces (floors, walls, props, etc), while sacrificing some health and ammo in order to do so. It is also essential to the process of market gardening, and by extention, Trollgier.
Have you seen some of the top Soldier players do rocket jumping? They go so far so fast!