These 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. You typically recieve 100 Assault Points from a failed Mission. You recieve 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 recieve 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 recieve an additional bonus added after the 10% for trading an armband, if they were the player that did so. 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 recieve an overall points deduction.