"The tremendous accelerations involved in the kind of spaceflight seen on Star Trek would instantly turn the crew to chunky salsa unless there was some kind of heavy-duty protection. Hence, the inertial damping field."
Star Trek: The Next Generation Technical Manual, page 24.
"Down in the cargo bay Dolby comments that it might be the inertial dampeners failing. He doesn't sound very worried given the severity of the problem, inertial dampeners are what prevent the immense forces of a ship acceleration or deceleration from being applied to the occupants. Well you know what this is like when you slam on the brakes or take a tight turn in a car that's going at a few dozen miles an hour, so imagine if you are travelling at the kinds of speeds a warp capable ship is. Inertial dampeners failing should be said in roughly the same tone of voice as 'MY ARM IS STUCK IN A WOOD CHIPPER!'."
SF Debris' review of Learning Curve