An AVR with multiple zones lets you simplify your life without having multiple amps all over your house.
Scenario 1: You want to set up a dedicated theater in a room, but want to do more common listening in your living room.
Scenario 2: Your watch movies on your 5.1 system in your living room, but want to setup a two channel system in bedroom for late night listening.
Scenario 3: You want to set up a good two channel system with higher quality full range speakers alongside your multichannel setup. or want to dedicated higher quality speakers for two channel listening.
A good AVR can be used in all the above scenarios to setup a good system without stacking components over components all over the house. You can designate your living room as Zone 1, your bedroom as Zone 2 and so on. Possibilities are endless, depending on the way it is implemented in your AVR.