Soundproof prevents all the effects of sound moves on the ability holder, granting them immunity from them. In Pokémon FireRed and LeafGreen, the Poké Flute cannot be used to wake up a sleeping Pokémon with this ability.
In generation III, there was an unused ability called Cacophony that had the same exact effect as Soundproof. It has been surmised that the Whismur family was supposed to get this ability instead.