Assault Points are points you win for attempting and/or successfully completing Assault Missions. They are used to purchase a number of different items from the Assault Mission Givers or the Remnants Permit, which admits the carrier to Salvage. You typically receive 100 Assault Points from a failed Mission. You receive more for a successful completion—the amount varies for different Assault Missions.
On a victorious attempt, every mission will reward a certain amount of total points. This amount is divided by the amount of participants. The player who used the Assault Armband will receive an additional 10% that does not count as a part of the mission's total. In addition, if it is the player's first successful run of the particular Assault, they will receive an additional bonus. If they traded the armband, this bonus is added on top of that 10% bonus. These points, as well, do not count as a part of the mission total.
However, if the party is below the recommended level, they will receive an overall points deduction.