Taillights, brake lights, or tail lights, (there is no official or correct version/name) are the red rear lights on a vehicle which either light up or get brighter when the brake pedal is pressed. Many of them also contain the rear turn signal lights as well. Working tail lights are mandatory on all vehicles in most regions, and some regions also govern the hight, location, and brightness of them.
Why are Tail Lights Red?
These lights are red because it's the color which most quickly draws human attention, and having it a different color than the headlights helps drivers know which direction the vehicle is facing at night. In addition, most traffic-related objects which are red mean "stop" (red lights at an intersection, stop signs), and braking is the process which brings the vehicle to a stop, so a psychological connection is made when brake lights are seen.
Because of the importance of the red in determining a vehicle's direction in poor visibility environments, having headlights in any shade of red is illegal in many regions.
Tinted Brake Lights
Some aftermarket companies sell tinted taillights which appear to be dark red or completely black. These are designed and bought for aesthetic purposes, and aren't road legal in some regions. Some of them are less bright than their fully transparent counterparts, but are often fitted with upgraded lights to overcome the difference.