Front and rear bumpers are designed to be both aerodynamic and to absorb some of the sudden forces in a collision.
Early bumpers were an additional piece of metal added to the front of the car, sometimes with rubber supports. Many modern bumpers are hidden just beneath the vehicle's body, and are made of layers of foam and collapsable metal. They are designed with safety in mind, and sometimes even enhance the structural rigidity of the vehicle. The extra layer(s) a bumper provides keeps the driver and passengers from feeling the entire force of a crash at one small point in time, and that spreading of the forces may mean the difference between life and death in many instances.
The photo at the left is of a 2001 Pontiac Grand Prix with the front bumper and headlights removed. With the aesthetic part removed, the inner section can be seen, such as some crash structure and the hood latch. The aesthetic portion also distinguishes this vehicle from other GM W-body vehicles, which may have different grille designs; the large openings to the radiator allow different designs to be made without airflow paths being blocked with some designs.
The picture at the right is of a front bumper of a 2001 Pontiac Grand Prix. The whole bumper assembly comes off for service, painting, or replacement of damaged parts. In this instance, the bumper was removed to paint the lower section black. Bumpers are meant to be replaced, and can sometimes be replaced with a bumper of a different trim level. For example, this bumper was originally only found on more expensive models, with the base model SE getting a different front bumper. Rear bumpers are also able to be swapped from time to time, but there may be issues with exhaust tip placement/count that would need to be considered.
Some governments of the world regulate how high bumpers must be, which sometimes limits car designs (such is the case with very small cars in the United States). Having bumpers at generally the same height is good for safety, but only by a small amount (assuming that size and type of car wouldn't have been designed that way anyway).
Racing vehicles have various types of bumpers, for safety and other advantages, such as brush guards in rally events.
Replacing a Front Bumper
This quick Cars Simplified video hosted by Steve shows how to remove the front bumper on a Pontiac GTO. This video was published February 15th, 2018, and the intro music is by Futures Passed.