Sonic damage - sometimes also called concussive damage - is one of the 8 damage types in the game. It includes damage from "powerful concussive forces and extreme-decibel sounds".
Sonic damage is usually most effective against non-Bane biological lifeforms. Sonic damage is also most effective against shielded targets, shields, and targets that carry hand-held energy shields. Sonic damage is least effective against lifeforms with armor, which includes Bane Soldiers and all types of Machina. Sonic damage has a bonus to knockback, and can cause a knockback even if the player has not applied enough attribute points to the weapon training to gain that effect.
For more detailed information about the effects of damage, see: Damage type