In Star Trek, inertial dampers are devices that generate an Inertial Dampning Field System (IDF)  to counter the effects of rapid acceleration and deceleration of a vessel by sustaining and absorbing the natural inertia of a vessel as it either moves through space. Acceleration effects are anticipated by computers, and the IDF is distorted along a vector diametrically opposed to the velocity change, thereby nullifying the force. If a starship were to jump to warp speed without using inertial dampers, the members of the crew would almost certainly die as the rapid acceleration would throw them back in to the consoles and rear walls killing them instantly. Conversely, they would also be killed if a ship were to come out of warp but in this instance the crew would be thrown forward. The IDF works parallel to the ship's structural integrity field (SIF, which augments the mechanical integrity of the ship's space frame).

The Star Trek The Next Generation Technical
Manual's illustration of the workings of the IDF

Inertial dampeners are necessary in Star Trek because, unlike real-life spacecraft, the crew in a starship do not operate in zero or micro-gravity but have artificial gravity systems. Real-life astronauts operate in zero or mico-gravity and would not experience any acceleration or decelaration forces except on launch from or re-entry into the Earth's atmosphere. A spacecraft in orbit around the Earth is typically travelling at 17,000 miles per hour but the crew inside the vessel are also travelling at the same speed, so they feel no forces acting on them. However, in reaching that speed, the vessel and crew had to accelerate from stationary (on the ground) to orbital speed in only a few minutes. In the case of the Space Shuttle, this acceleration is around 3 times the force of gravity - 3g - making the crew feel three times their normal weight.

To counteract these g-forces, protection is provided not by inertial dampeners but by a specially designed outfit, called an anti-g suit, which supplies pressure to the abdomen and legs, thus counteracting the tendency for blood to accumulate in those areas. Seating in the craft is also designed to provide proper support to te body, especially the head. While facing backward in a seated position, properly supported human test subjects have been able to tolerate a deceleration force of 50 g without severe injury.

Typical acceleration changes from launch to orbit