You want in depth? I'll give you in depth. Hope you can keep up.
DI-http://smashboards.com/showthread.php?t=60218
Hitbox- there are two types of hitboxes:
Character hitboxes-this determines "where your character is." If this hit box is hit then you will take damage.
Attack hitboxes-these determine the range of attacks. If this hits a character hitbox then that character takes damage. If this hitbox hits another attack hitbox then one of two things will happen. If a ground attack hitbox (excluding some specials) hits another ground hitbox, then they clank. If it hits an aerial hitbox hits another hitbox, they both just continue going.
Disjointed hitboxes-this is just a fancy way for saying that the attack hitbox of a move hits far away from the character hitbox of that character. For instance, Marth's sword is a disjointed hitbox. That means that while Marth is attacking with his sword, every part of that sword acts like an attack hitbox. In order to hit a character you must reach their character hitbox, not their attack hitbox and thus you have a lot of distance where Marth is safe thanks to his sword.
Priority-this term is used to describe how likely an attack is to hit a character through their attack. This takes advantage of both the size of the attack hitbox in relation to the character (its disjointedness) and the type of attack it is (aerials don't clank, so they will continue moving until either you or your opponent is hit.) A move out prioritizes another move if the attack hitbox of that move is large enough to reach the opponent without exposing the user's character hitbox to the opponent's attack hitbox. A move is said to have high priority if it out prioritizes a lot of other moves.
So there's your in depth explanation. Hope it helps. But next time, use the search function.