Amplifiers convert a low level signal from your head unit to a powered signal for your speakers. That's about it.
Most head units have a small amp built in. Usually about 50 to 80 watts RMS.
For most people, the built in amp in your head unit will be sufficient. The only time that you would need an amp is if you are unhappy with the volume and clarity of the sound system in your car. With the addition of signal processors and amplifiers, you can "tune" the sound system to only play the frequencies that you want, at the level that you want.
The only other time that you would absolutely need an amp is if you are adding a subwoofer. Subwoofers are only made to play low frequency signals, a crossover network is a must. Also, they usually need far more power, to recreate the frequencies that they play, than a head unit can give.
Hopefully this helps you out in making a decision about adding an amp to your car.
