What is the basic difference between AM and FM radio?
Short answer: FM is far less susceptible to disturbance of the signal.  



This is an AM modulated signal. The contours are the baseband signal which we recover by demodulation. Notice that there's a spike in the signal, which may be caused by a thunderstorm for instance.



This is the demodulated signal. The demodulator doesn't "know" that the spike isn't actual part of the signal, so it can't remove it, and the listener will hear a tick in the symphony she's listening to.

FM has a constant amplitude, and the demodulator won't be fooled by spikes in amplitude since it will detect variations in frequency.



This is an FM signal. The baseband signal determines the change in frequency of the carrier. Notice that the spike doesn't change the frequency, so it won't be audible after demodulation.