Invincibility is a state during which a character cannot be attacked or damaged. Attacks will hit (so the attacker takes hitlag), but will not deal damage, knockback, or hitstun. Characters who are invincible can still be affected by certain windboxes, as well as Master Giant's grab attack in Smash 4.
Invincibility's negative aspect is that on the Planet Zebes, Brinstar, and Norfair stages, characters will fall straight through the stage's lower hazard, rather than sustaining damage and bouncing back up. They may occasionally also be KO'd if they are standing on the track on Port Town Aero Dive, and both the Melee Mute City and the Smash 3DS Mute City.
In Super Smash Bros. Melee's debug menu, invincibility is displayed by affected hurtboxes changing from their usual yellow color to a green color during the invincibility period. A similar feature is present in Super Smash Bros. Ultimate's Training Mode via an invincibility toggle, which causes invincible parts of characters to acquire a green tint.
Invincibility should not be confused with intangibility or armor. During invincibility, all knockback and damage is canceled when the character is hit. In regards to intangibility, however, the character cannot be affected by either knockback or damage in the first place. Armor has characters sustain damage, but not knockback.