Airsoft refers to a class of replica air powered guns that originated from Japan (although the origins go back to the US in the 70s). The power levels are way below those of usual airguns, but the guns are 1:1 scale copies of original pistols, rather than original designs.
Airsoft, like paintball has a devout following not only by civilians, but is used by law enforcement to train in scenarios where real firearms just aren't practical: schools, airplanes, close quarters, etc