Mags in a nutshell:
Mags increase your stats and give you access to Photon Blasts. Feeding a mag a consumable item will increase its stats, which in turn, increases your stats.
Mags can augment four different stats: Def, Pow, Dex, and Mind.
Mags can reach a maximum level of 200. For every level a mag has in def, it will increase your character's def by 1. Likewise, pow and mind have a 1-to-2 correspondence, whereas dex has a 2-to-1 correspondence. (That is, 2 levels in dex for the mag = 1 point increase in dex for your character, and 1 level in pow = 2 point increase in atp. Note that 1 level in dex does not count towards any increase in stat).
Ex. a level 200 mag has the following stats:
This mag would give + 20 DFP, + 200 ATP, + 25 ATA, + 60 MST
Mags evolve at level 10, 35, and 50 and will obtain a photon blast at each evolution. You might want to look at some of the guides here to determine what kind of a mag you would like to build:
Best of Luck!