Magic are not earned through some activity or purchased from shops, they are drawn from certain Draw Points or drawn from monsters in battle.  When drawing in battle, you can either use the magic immediately or stored for later use.  The magic you stored are to be junctioned, unless you want to get KO'd all the time in battle.  Not junctioning is like not using materia in FF7. 

The purpose of junctioning is to enhance the power of party member's Strength, Speed, Vitality, spirit, etc.  You can also junction magic to Elemental and Status propeties.  For example, if you junction Fire to Elemental Attack, when you attack, depending on your percentage, the element Firewill enhance the power of the attack.  Another example is when you junction Sleepto your Status Defence, depending on your percentage of Sleep spells, you will be immune to Sleepwhen your enemy uses it on you. 

How much percentage you will have in junction magic is important.  If you junction 30 Protectson vitality, your vitality will be higher then junctioning just 10 Protects.And if you junction 80 Berserkto Status Attack, you will have more chances or beserking your enemies then just junctioning 40 Berserks.

Also, the power of magic is important, eg. junctioning 10 Blizzagas to Elemental Defencewill be better then junctioning 10 Blizzaras. And also the compatibility of magic, eg. junctioning Shell to Spirit is better then junctioning Sleep to Spirit.

Of course, all the junction abilities has to be from a GF you have junctioned.  For example, you can't junction to Status Defence if none of the junctioned GFs has the ability.  You can buy abilities from PET STORES, but some GFs initially learned the ability.