Secondary Magic is a magic that is bought at the magic shop. You check the "Secondary Magic" box and purchase the magic, giving you secondary magic. However, the price of a secondary magic costs 2.5 more than buying the magic as a primary. (ex: Archive Magic costs 45,000 jewels but 112,500 jewels as a secondary.) Buying a secondary will give you only four spells so it is recommended to buy a secondary that will create good combos with your primary magic.
Glitch: After buying your secondary magic, you will receive all the spells. To fix this, you can simply reset.