Intangibility is a state in which characters will not be hit by attacks. Attacks will simply not affect intangible targets at all, as if they were not there at all. Intangibility is often attributed to dodges, techs, edge-grabbing, get-up attacks and animations, certain body parts during certain moves, and the start of a shield break. Since the character is not hit, a long-lasting attack (or very short intangibility time) may still hit the character once it ends.
Intangibility'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, possibly causing an otherwise preventable KO. They may occasionally also be KO'd if they are standing on the track on Mute City (SSBM), Port Town Aero Dive or Mute City SNES. In Smash 4, Master Giant's "glowing hands" attack also completely ignores any form of intangibility as well as invincibility (including respawn).
In Super Smash Bros. Melee's debug menu, intangibility is displayed by affected hurtboxes changing from their usual yellow color to a blue color during the intangibility period. A similar feature is present in Super Smash Bros. Ultimate's Training Mode via an invincibility toggle, which causes intangible parts of characters to acquire a blue tint.
Intangibility should not be confused with invincibility. In intangibility, characters can not be affected by attacks at all but in invincibility, characters can be hit by attacks but they will not take any damage or knockback.