Air friction is a measure of how long it takes for a character to stop moving from a sideways force when in midair. It is the aerial equivalent to traction, which only applies when grounded.
Air friction only applies when the player is not holding the Control Stick in a horizontal direction (or the input is being ignored, such as when in hitstun). If the player is attempting to slow down, air acceleration applies instead, and air friction is ignored. This allows characters to be designed with several properties:
Air friction also determines how far a character travels when they are aerial grab released (along with gravity in Melee and Brawl). A character with low air friction will travel a long horizontal distance whereas characters with high air friction will not travel far at all. This is because air friction acts as a force against the momentum granted by the aerial grab release. This results in characters with higher air friction being left in a more vulnerable position after being aerial grab released. This is especially significant in Brawl, due to the long amount of time the grab released opponent cannot act. Characters with high air friction in Brawl are much more vulnerable to aerial grab release followups (unless they have extremely high gravity to compensate), especially if they can be forced into an aerial grab release from the ground. This is the reason why Wario's aerial grab release in Brawl sends him nowhere horizontally, making him extremely vulnerable to followups.
It is circumstantial as to whether high or low air friction is good or bad and it is also game dependent (as with the aforementioned Brawl aerial grab release example). Low air friction means a character will not slow down as much if the player attempts to use a neutral aerial when moving, and will cause them to travel a bit further during combos. But on the other hand, high air friction helps resist being KO'd to a degree, and it may be beneficial in some cases to slow to a stop quicker without providing directional input.
Air friction values
Super Smash Bros.
Super Smash Bros. Melee
Super Smash Bros. Brawl
Super Smash Bros. 4
* Ryu is a special case. In most circumstances, his air friction is a standard 0.015. However, when he jumps, his air friction is 0, meaning he will not slow down at all unless the player attempts to decelerate.