Teching is useful because it gives intangibility and allows to act faster after the fall.
The word "ukemi" refers to a rolling technique used in Japanese martial arts when taking an attack. The name has found its way into several (mostly fighting) games, such as the Soul series, to describe similar fall recovery moves.
The word "tech" is borrowed from the competitive communities of other fighting games and traces its origin back to technical bonuses awarded in Capcom games for performing special maneuvers to escape grab attacks and get much less damage and more recovery time.
Unlike a lot of other techniques, teching has been a mechanic in every Smash Bros. game.
Types of Techings
Standard teching, or neutral teching, is a neutral ground-based tech performed by pressing a shield button when a tumbling character comes in contact with the floor. The character will experience a brief period of invincibility, and will quickly bounce from the ground into a standing animation. The player will grab any items that he or she comes in contact with. This is the easiest tech to do, and is commonly done, even by casual players.
Roll teching, is a ground-based tech performed by tilting the control stick left or right when teching. The character will bounce from the ground into a roll-like animation during which the character moves left or right while invincible. This can allow characters to roll away from their impact point to complicate tech chasing, but rolling against an edge will halt the roll's sideways movement.
Wall teching is a tech against a wall. To wall tech, the player must press a shield button 20 frames or fewer before hitting the wall while tumbling, reeling, or in hitstun. 20 frames after each press is a 40 frame downtime window where a wall tech cannot be done, so button mashing reduces the player's likelihood of teching. As with normal techs, the wall teching character experiences a few invincibility frames, and the tech absorbs the player's momentum.
Ledge teching is when a recovering character can use a form of wall tech to survive an edge-guarder. If the recovering character is hit with an attack very near to the ledge, he or she can smash DI towards the ledge and wall tech to absorb all the knockback of the enemy's attack. This is usually performed by pressing the shield button to wall tech before pressing the control stick to DI, because of the 20 frame window in which the player can input the tech before hitting the wall.
Wall Jump Teching
If a jump input is active when a wall tech is performed (such as holding Up or pressing a jump button), then the teching character will wall jump. Every character can wall jump tech, even those who cannot wall jump normally. A skilled player can survive a meteor smash (such as the Ice Climbers' forward aerial that often ends their chaingrabs) by wall jumping teching.
Celling teching, is a tech against a ceiling. To ceiling tech, the player must press the shield button 20 frames or fewer before hitting the ceiling, while in hitstun. 20 frames after each press is a 40 frame downtime window where a ceiling tech cannot be done, so mashing buttons reduces the player's likelihood of teching. As with normal techs, the ceiling teching character experiences a few invincibility frames, and the tech absorbs most of the momentum. It is shown on the Super Smash Bros. Brawl tutorial video on the Nintendo Channel that it can even save a character at 999%. There are few situations where there is a ceiling for a player to tech off of, but it can happen quite frequently in caves in some stages.