A midair jump, commonly referred to as a "double jump", is a jump that can be used once every time the user is airborne. Just like the single jump, double jumping is achieved by hitting up on the d-pad/control stick or hitting the jump button.
Overview
Double jumps are a lot more varied in animation than single jumps. Some characters twist, others flip, and there are some double jumps that do something completely different. Like jumps from the ground, characters have a different animation if they are jumping backwards. For example, Mario spins around when performing a regular midair jump, but does rapid backward somersaults when performing a backwards midair jump. If a character flips, their collision bubble moves accordingly, but this hardly has an effect on the jump. There is always the slim chance that it could narrowly avoid an attack, but very unlikely considering most hitboxes are round.
Certain characters can inflate themselves (Kirby, Jigglypuff, King Dedede) or flap their wings (Meta Knight, Charizard, Pit) to jump multiple times in the air. Characters with multi-jumps can turn around when in midair by using them. These multi-jumps become useless (or nearly useless for some) if the character is metal. Characters with Multi-Jumps have good air speed (with the exception of Meta Knight and King Dedede) and are usually light-weight (with the exception of Wario, Charizard, and King Dedede).
Yoshi's double jump is unique in that it provides a healthy amount of knockback-based launch resistance.