Similar to an amp (you typically wouldn't have a receiver *and* an amp). The difference is that an amp receives an analog signal, and amplifies it for the loudspeakers. A receiver can take any type of signal, analog or digital, decode it (or translate it into 1 or more analog channels) and amplify it for the loudspeakers.

Basically, an amplifier is just a volume control. A receiver is a home-cinema amplifier, capable of surround sound in   Dolby Digital,   DTS or any other format.