The tail light lens is specifically the multi-colored plastic piece on the outside of the car. The lens is usually one piece and covers the entire light. On older cars, they tended to be small and circular or rectangular but on more modern vehicles they are often larger and may be irregular in shape. As mandated by law, there are different colors for the different light functions. Red is for the stop lights, yellow or amber is used for the turn signals (or directional lights), and white or clear is used for the reverse lights. There may also be fog lights or parking lights on some cars. A car will drive fine without the tail light lens but they are required for state inspections and you may be ticketed or pulled over if they are missing. A visual inspection is often all you need to know if you need a new lens. Lenses can become broken or cracked do to impact or wear. It may become scuffed or oxidized making it difficult to see. Water can also leak in through the crack or missing lens and may cause further damage to the light or to the car by seeping into the truck or causing rust.
The tail light lens is just one piece of the tail light. They are available separately in most cases but may be only available with the entire assembly. They were once small lantern shape devices that became integrated with the body of the car in the 1940s. There size and placement has often been dictated by local laws. It is common to see the same vehicle with different tail light lenses in other countries do to their legal and safety requirements. They are usually made of translucent plastic but some older types may be made of glass. They also have an important styling function in transmitting the image of the car.
If you are the do-it-yourself type you can try to change out the tail light lens yourself. Below are some basic instructions for changing the lens. It is not vehicle specific. Make sure that you have the car in a safe well-lit place and you have the right tools before trying to save the light.