It's simple physics, Newton's first law of motion: A body at rest will remain at rest unless an outside force acts on it.
Think of it this way: If you're not wearing a seat belt on an airplane that drops suddenly — which often happens with turbulence — you're the one at rest. You'll stay at rest as the plane, very literally, drops out from under you. If you're strapped in, the seat belt serves as an outside force acting on you, taking you with the plane as it drops and saving you from bonking your head on that overhead bin above you.
"It allows you to stay in place and ride along with the airplane," McSpadden says. "It's just that added safety margin that if something unexpected happens, you're still going to stay with the airplane."