If the Pokémon holding this item creates rain with the move Rain Dance or the Ability Drizzle, it lasts eight turns instead of five turns. (Prior to Generation VI, it has no effect on Drizzle, which creates rain with indefinite length in those games.)
In the Generation VII games, if rain has its duration extended by the Damp Rock, the turn counter on the user interface for these effects will indicate that it lasts for 8 turns for the player whose Pokémon used the move, while it will display that it lasts for 5 turns for their opponent. After 5 turns of rain have passed, the user interface will display that it lasts for 8 turns for both players.