You've seen diagrams explaining AM:
* signal (varying amplitude),
* carrier (constant amplitude),
* and carrier "slowly" changing amplitude according to amplitude of signal.
As for what is a suitable minimum carrier-to-signal ratio? I guess 10x. Our eyes can easily recognize a signal is riding the carrier. Notice that the lowest station on the AM band is around 500 kHz. That is adequate for carrying audio up to 10 kHz. 10k is the separation from one commercial station to the next.