Invincibility

Invincibility is a period of time in the  series where a character is invulnerable to damage, knockback, hitstun, and grabs. An invincible character will be hit when attacked, but the attack will have no effect on them. However, they are still vulnerable to taking recoil damage from any attack that deals it.

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 execute their attack to prevent interruption.

Invincibility frames are not to be confused with knockback resistance, which only reduces or negates the effect of knockback — not damage — from an attack.

Intangibility
Intangibility, also known as dodging invincibility, is very similar to invincibility in that characters cannot be dealt damage, knocked back, or grabbed. The main difference, however, is that intangible characters will not be hit by attacks at all. For example, a projectile will travel right through them.

Intangibility is often attributed to sidesteps, techs, ledge attacks, floor attacks, and certain body parts during specific moves, such as 's up smash. Since the character is not hit, a long-lasting attack — or a very short intangibility time — can cause a character to get hit regardless once the intangibility wears off.

Trivia

 * In the original Super Smash Flash, the only time characters get invincibility frames is when they spawn back to the stage after getting KO'ed. Otherwise, they are practically non-existent.
 * Because of how invincibility frames are currently treated in Super Smash Flash 2, a character under them will be unable to get a Super Star, a Super Mushroom or Poison Mushroom event if they were directly touched. This flaw is more evident if the invincibility was granted by a Super Star itself. This makes it possible to attack the hitboxes of the aforementioned items, making possible to launch them.