The walljump is a trick that allows for many sequence breaks, and is important to master for speedrunning.
To perform a walljump, start a spinjump against a wall. Press away from the wall, and press jump soon after. The window for pressing jump will depend on your location relative to the wall and various other conditions, but the window is normally between two and ten frames after you press away from the wall.
A series of successive walljumps in Parlor:
There are several instances where continually walljumping against the same wall will be useful. In those cases, you will want to press against the wall after completing the walljump.
A series of successive walljumps against the same wall in Climb:
If you perform a walljump and, while continuing to hold jump, press down on the directional pad with Morphing Ball enabled, you will immediately morph, meaning you do not have to press down twice to morph. This helps with the Alcatraz escape in particular.
If you perform a walljump and, while continuing to hold jump, press up on the directional pad, you will not break out of spin. You can only break out of spin in this manner after walljumping if you let go of jump or turn around.
If you are in a pseudo-Screw, you can release the shot button to remain in a spinjump after walljumping.
There are some walljumps where an overhanging ledge will make it so that you need to jump in the later part of the frame window in order to then walljump on the side of the overhang. Examples include The Worst Room In The Game, the upper left side of Bubble Mountain, and Plasma Room.