A double jump is a mid-air 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 control pad/stick or hitting the jump button.
Double jumps are a lot more varied than single jumps. Some characters twist, others flip, and there are some double jumps that do something completely different. If a character flips, his or her collision bubble moves accordingly, but this hardly has an effect on the jump. There is always the slim chance that it could narowly avoid an attack, but very unlikely considering most hitboxes are round.
Certain characters can inflate themselves (Kirby, Jigglypuff, Dedede) or flap their wings (Meta Knight, Charizard, Pit) to jump multiple times in the air. These multi-jumps become useless if the character is metal.
How Characters Double Jump
The nature of double jumps may seem strange with many characters, as most of the characters in the Smash Bros. series are incapable of double jumping in their own games. However, upon close observation, players may notice a slight ripple appearing underneath a character right after he or she double jumps. It can be concluded that when a character double jumps, a small, invisible platform appears for the character to jump off briefly, giving them a slight boost. Characters like Jigglypuff, King Dedede and Kirby, who can puff themselves up to fly higher without the use of a platform, do not use the platform. The new Brawl characters with wings, Pit, Meta Knight, and Charizard, also do not use the platform, but simply flap their wings.