Cheek Pouch restores 33% of the Pokémon's maximum HP when it consumes a Berry, after the effect of the Berry is applied.
Cheek Pouch activates even if the Pokémon eats another Pokémon's held Berry via Bug Bite, Pluck or Fling, but only if the Berry is actually eaten for an effect (i.e. the Berry consumption animation plays). Consuming a Berry through other means (such as Natural Gift, using Fling, or its Trainer giving it a Berry from the Bag) will not trigger Cheek Pouch.
Cheek Pouch will not activate if the Pokémon is under the effect of Heal Block.
Outside of battle
It is unknown if Cheek Pouch has an effect outside of battle.
When a Pokémon with this Ability eats a food item, Berry, Seed or health drink, the Pokémon will recover 25 HP. An enemy Pokémon with this Ability will spawn holding a Seed, regardless of whenever or not there are any items available on the floor. Sometimes, it may hold a Tiny Reviver Seed or a Reviver Seed, in which case, the enemy Pokémon will use it upon fainting, turning it into a Plain Seed.