Strengthen your heroes by filling in equipment spots. "Green plus sign" means you can equip your hero with equipment. Once all slots are full, you can "Promote" your hero to permanently add the stats from the equipment to your hero. 

Heroes can be promoted from green or blue to purple. You need to earn all six items your hero needs and equip all of them, then click the "Promote" button until the hero's level is raised to purple.

Note: Once you have equipped a hero with an equipment, you cannot unequip the item.