A mag is a small familiar like robot that follows you and provides stat buffs.
In Order to use the mag you need the license from Cofy who is the second girl at the mission counter in the main gateway.
The mag menu can be found on your inventory screen.
Leveling one to level 30 by feeding it unwanted items or weapons will unlock it's Photon Blast Ability.
From the Sub-palette you can add the Photon Blast ability to your item tray.
Then defeat enemies until the Blast is fully charged. Your mag will glow when it's ready.