Reflection is a phenomenon wherein one fighter gains control of an enemy's projectile and uses it as their own attack. Most, but not all projectiles reverse direction upon being reflected, sending them back to their original users.
To be reflected, a projectile must come into contact with an attack or object that reflects, such as the aptly-named Reflector, Ness's forward smash, or a character wearing a Franklin Badge. Most reflectors increase the damage done by projectiles, while some also increase their speed. Projectiles can be reflected from any direction, and can be reflected multiple times to multiplicatively increase the damage dealt.
In SSB64 and Melee, if a projectile is too strong for a reflector, the reflector breaks as if it was a shield and stuns its user. From Brawl onwards, the projectile simply ignores the reflector and hits its user anyway. In the case of Ness's or Lucas's forward smash, should the overpowered projectile collide with the move's hitbox without striking the user, he will undergo a proportionally-substantial amount of lag due to being outprioritized.
Reflectors are generally very useful moves, as they help prevent projectile camping and spamming. As such, characters with reliable reflectors tend to have better matchups against characters that rely upon projectiles, such as Samus, than those who lack a reliable reflector.
In addition to the above, Villager and Isabelle are able to grab projectiles and items and store them for later use via Pocket. While not strictly a reflector, retrieved projectiles gain a 1.9x damage multiplier generally associated with reflectors.
In Ultimate, a visual indicator in the form of a flashing blue hexagon (referencing Fox's Reflector) was added to all reflecting moves when struck by a projectile as an indicator that the item was reflected with the damage multiplier appended accordingly.
List of reflectors
Reflectors only available as custom moves are in italics.
List of reflectable attacks