Bleedthrough in Halo: Reach is a term that describes how the game handles excess damage from melee attacks onto shields. In its most basic sense, it means you do not need to entirely remove an opponent’s shield before you can one-hit kill them with a melee attack.
When you are loading into the multiplayer modes, you will often see a message on the screen talking about bleed through being enabled. The note means that any excess damage from a melee attack will be passed on to an opponent’s health after the shield is broken.
When bleed through is not active, even someone only has a small amount of shield left, and you melee them, the melee attack will break the shield, but any excess damage leftover will be lost, not passed on to their health bar. The process means you cannot hit a low shield enemy with a melee attack and then have the excess damage apply to their health and kill them.
It has a direct effect on how people will play the game and the tactics that they will use in multiplayer modes. When bleed through is on, you will often see players rush each other, confident they can get the other person’s shield low enough to one-hit kill them with melee. When bleed through is off, people will often wait a little longer, sometimes even waiting to see their opponent’s shields pop before rushing them for the melee kill.