Instant attacks are attacks that happen as soon as you activate them, meaning they have no activation frames. Most moves, when you use them have a few frames of animation where your character is performing the attack, before it reaches a hittable state. Usually there's very few frames, but some big lug damage-dealing characters might have much slower moves. There are a couple attacks out there, however, that are defined as "instant," meaning they enter a hittable state as soon as you execute the attack. This also provides the extra benefit in that the attack cannot be interrupted; If your character gets hit as they do the attack, it will still come out.

I can't provide you with an exhaustive list, you'll have to check out the UMVC3 book guide for specifics, but I know a few of Dormammu's Liberation attacks are instant, as well as Phoenix Wright's Ace Attorney hyper combo.