Amp Limitation on 120v Circuit
In order to limit the current drawn from a 120v socket to 15A using ohms law, you make sure that the load you attach has a resistance of at least 8 ohms. 

However when you buy a kettle or toaster, it doesn't tend to say 'resistance 8 ohms' on the specification plate, it says '120v 15A'. So the simplest way to limit the current is to make sure that the rated current of the device you connect is less than 15A. 

There is a sort of 'contract' you have with the socket, it agrees to supply whatever current you choose to draw, and you agree to not try to draw more than its maximum.

The breaker is there to enforce this contract. If you try to draw significantly more than the rated current, it cuts you off.