Down (ダウン*)? is a special condition in the series.
Enemies inflicted with Down are knocked on the ground. In that state, they're unable to evade and the damage they take is increased (50% in P3/4, 25% in P5). The Down state can overlap with another status effect. In Persona 3 and Persona 4, Downed users are vulnerable to being inflicted with Dizzy.
Users that successfully Down will receive One More turn. For the player party, if all enemies are on the floor, normally they'll have the opportunity to perform an All-Out Attack, which will also automatically recover the Down state of all enemies. In Persona 5, this also opens opportunity to negotiating with the enemy.
In Persona 3 and Persona 3 FES, recovering from Down takes a turn, but in other games, users are able to act instantly on recovery.
Generally, Down is inflicted through exploiting the user's weakness, through critical hits, as well as during out-of-order Follow Ups. In Persona 3 and Persona 4, users that miss trying to perform a melee attack will be knocked down (unless in P3, the user yields a bow or a gun.) In Persona 5, Shinya Oda's Confidant ability, Down Shot, allows the protagonist to down an enemy using his ammo. In Persona 5 Royal, Technical attacks have a 50% chance of Downing their target. If the party increases their Technical rank, the odds will be increased in their favor: 67% if they're at rank 3, and 100% if it's rank 4.
In Persona 3 and Persona 4, the skill Re Patra can be used to help an ally recover from being knocked down.
Guarding protects the user from being Downed from having their weakness exploited.
In Persona 5 Royal, the skill Guiding Tendril downs all enemies in battle, but only works when the party's ambushed the enemy.