An Invincibility frame is a period of time where a character is completely invulnerable to damage, grabs, and knockback. Invincibility frames are not to be confused with knockback resistance, which only reduces or negates the effect of knockback - not damage - from an attack, or intangibility frames, where a player is, essentially, invincible, however will not receive hitlag if on the receiving end of an attack.
Characters can gain invincibility frames in a few ways. An example can be during the initial stages of a character entering their Final Form or using some other form of a Final Smash, which grants them invincibility frames as they transform or exceute their attack to prevent interruption.
A character with intangibility will not be hit by attacks. For example, a projectile will travel right through them. Intangibility is often attributed to dodges, techs, edge-grabbing, floor attacks and animations, and certain body parts during certain moves, such as Mario's up smash. Since the character is not hit, a long-lasting attack (or very short intangibility time) may still hit the character once it ends. Intangibility can also be called "dodging invincibility".