The ability holder takes 50% less damage from "sound-based" moves such as Boomburst, Overdrive, and Uproar. The power of these moves is boosted by 30% when used by the ability holder.
Soundproof works similarly to Punk Rock in that it also alters damage from sound-based moves. However, Soundproof gives the ability holder immunity to sound-based moves (as opposed to decreasing the damage) and doesn't increase damage from these moves when they are used by the ability holder.