Action Points or AP are the currency in battles, you get them automatically and can be upgraded in battle with more AP, Upgrading APs makes it Generate Faster and Have a larger maximum Action Points storage, it can also be upgraded with MSP outside the Missions in the Customize (Home) section.
AP level Edit
The AP per second (AP/s) values given in the table below are those after rescuing all the POWs in the stages that increase the AP in battle and upgrading the Development Speed Level base to the maximum. Each level increase the AP generator by 50% from the initial.
The Earliest built column is a recommandation of the fastest way to build the unit by their cost at the beginning of the mission. Those values are only taking account when the AP generator is upgraded as early as possible and everything is unlocked (cited above).
Example 1: if the unit to build costs 200 AP, it is better to upgrade the base to level 1 because this one is more optimized for building an unit that has the price between 120 and 320.
Example 2: if the unit to build costs 120 AP, it is better to upgrade the base to the level 1 even though both the level 0 and 1 would reach 120 AP at the same time but after building the unit, the base level 1 would have an advantage over the level 0.