Stance mirroring
Stance mirroring is a mechanic in which most or all of a character's animations (including attacks) are mirrored if they turn around, mimicking the sprite mirroring of classic fighting games. The purpose of the mechanic is so characters face the screen more often. When mirrored, all hitboxes are also mirrored - for example, when Mario throws a punch when mirrored, the hitbox will appear on the opposite arm than it is normally defined as being attached to.
In general, a character must have a symmetrical body and not wield a weapon in order to be eligible for stance mirroring, though the weapon restriction was relaxed for many characters in Ultimate if they don't wield it at all times (e.g. Villager's various tools). Minor differences such as Pikachu's tail and K. Rool's eye tic can be acceptable, depending on their exact animations and hurtboxes. In general, characters in Ultimate are animated more with stance mirroring in mind compared to SSB4.
Stance mirroring also affects which hand characters use to hold, swing, and throw items. Turning around will cause a held item to simply teleport to the other hand (there is no animation for it). Similarly, if a character is reversed by Mario's Cape or such, they will complete their rotation before they snap into their mirrored pose.
As some characters mirror while others do not, it is possible for interactions to differ based on whether the characters are facing each other left-to-right versus right-to-left. For example, a mirroring character's thin attack may hit a Marth's extended sword arm from one direction, but not the other.
Stance mirroring is not present in games before SSB4, though certain special moves and taunts in Melee and Brawl would choose between two different animations based on facing direction to mimic the effect.