Air dodge

Air dodging is a technique in Super Smash Bros. Melee and Super Smash Bros. Brawl. As its name suggests, it allows a player to dodge attacks in midair.

Melee

In Melee, an air dodge is performed by fully pressing either the L or R button while in the air. If no direction is held, the character will stop in midair, while holding a direction causes the character to move in that direction. In both situations, the character will get some frames of invincibility (the "dodge") - but after the dodge is finished, they become helpless. It can also be used as a recovery move, but the short distance traveled makes it somewhat ineffective.
Airdodging in a downward direction will bring you in contact with the ground, which can cause a character to slide a distance on the ground. Depending on the angle of the dodge, the traction of the character on the ground and your height from the ground. This is known as wavedashing.

Brawl

Air dodging is also included in Brawl, but it has been completely revamped. Instead of going in whatever direction the control stick is pressed, air dodging simply moves the character in the same direction their momentum is already taking them. The timing of the air dodge is slightly different, with most air dodges lasting less time than in Brawl. Most notably, air dodging no longer puts a character in a helpless state, but allows the character to perform any attacks, second jumps, or even another air dodge in the same jump.