Intangibility means the hurtboxes on a fighter or limb don’t interact with the hitboxes of other fighters. If something slashes past, it’s like an intangible fighter isn’t there. Fighters are fully intangible head-to-toe during dodges, whether on the spot or rolling. Fighters are also fully intangible the first time they ledge-hang during an airborne period. Often, a fighter with long-reaching pokes has an intangible fist or forearm, reducing the likelihood that this attack will lose head-on encounters. Headbutting fighters are often blessed with an intangible noggin. This is one of several properties and mechanics that lead people to say a move has good priority.
In Training Mode, there’s an option to make visible when limbs and fighters are intangible, and we strongly recommend you enable it. Intangible hurtboxes are shown as blue bubbles. (The easiest way to see this is to sidestep or roll.)