Magic plays a vital role in Final Fantasy VI. The basis of the plot revolves around the idea and misuse of it, and in-game mechanics are heavily dependent on Magicite from Espers which not only boost your stats, but also give you the ability to learn spells to cause damage, heal yourself and make your life easier in the long run.
To learn Magic you must equip an Esper and keep it quipped until you learn the ability. You can switch Espers without having learned abilities. You will also learn the abilities at different speeds.