At the end of every turn the Pokémon with this ability is out, the Pokémon's speed increases by one stage. It does not activate if the user was just switched in.
Pokémon Mystery Dungeon
Originally, this ability provided the Pokémon with this ability to get a boost to their movement speed every 250 turns. In Pokémon Super Mystery Dungeon, this was changed so it increases after the first turn and every 20 turns later but the speed boost wears off after 5 turns.