Basically...
Hitboxes - the areas of an attack which deal damage
also can be used to describe areas on a character which receive damage (in FPS), but since in SSB characters receive damage all over - no point.
A disjointed hitbox is a hitbox which is seperate from the character ie. Marth's sword, Mario's Fsmash fire. Advantages of a disjointed hitbox is of course that you can't take damage on them, and they go thorugh more stuff (in melee, marth's Dtilt could be used to poke through the stage).
Priority- when two moves connect at the same time
which one is applied first. Work the rest out. If the Dair you are doing has a hitbox which connects with the enemy before their upsmash does, then your Dair wins. But if they connect at the same time., it's the one with the highest priority. Which, in many cases, may be upsmash.