Battle Drops are items received from defeating enemies in battle.
When an enemy is defeated in battle, the party has a chance to receive an item. The item that can be received is assigned to the demon at hand. For example, in Shin Megami Tensei, Jack Frost can only drop "Mabufu Stone" upon being defeated.
The property of dropping items is generally exclusive to encounters, and bosses and mini-bosses generally don't drop anything. Although, there are numerous encounter enemies that yield nothing as well.
In Persona 5, Shadows can only drop material items (with the exception of the Reaper, who drops a Divine Pillar, an accessory,) although in Persona 5 Royal, some enemies may instead drop sooty armor. On principle, Shadows in the Depths of Mementos and the Qliphoth World do not drop any items after being slain, with the exception of Abaddon in Royal, who drops a Sooty Gilded Collar.
In Persona 5 Royal, the protagonist can consult Jose to permanently boost the drop reward in Mementos specifically, in exchange for Flowers. If affected, enemies inside Mementos will drop more of the same item, all the way to 11 in a row. For more information on the subject, see Jose's Shop.