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Deals damage. In-game it allows you to travel across water.
As one of the two competitive HM moves, sporting high Base Power and perfect accuracy, Surf is available to almost every Water-type Pokémon and is often their main special STAB attack. However, due to the non-comprehensive coverage of Water-type attacks, it should not be the only damaging move in the moveset, or its user is easily walled by Grass-, Dragon-, and other Water-type Pokemon.
Hydro Pump is a much more powerful alternative, but it has lower accuracy and fewer PP.