The roof aerial receives radio waves so that you can listen to the radio in your car.
The roof mounted aerial fixes to the roof of your car and you can buy either a retractable or non-retractable aerial. Retractable roof mounted aerials can be extended fully or retracted back into the body of the car, which is a useful function making it less likely to be damaged by corrosion due to the weather or broken off accidentally.
The roof aerial is connected to the car stereo by an aerial cable which houses the conductor needed to receive radio reception, and is basically an extension of the center conductor inside the aerial cable.
The roof aerial may, of course, get damaged or simply over a long period of use suffer general wear and tear and will need replacing. A roof aerial will usually last between 4-6 years before you need to buy a new one. If the roof aerial snaps then you will, of course, need to buy a new one. If there is no obvious damage to the roof aerial but you are experiencing poor reception and sound quality which is getting worse over time, then this is a sign that you need to replace the roof aerial. It is possible that your car will still be able to receive FM radio when the roof aerial has stopped working but if your car is unable to pick up a signal on the AM frequency then it is very likely the aerial is broken.