Multi-zone gives you the opportunity to enjoy music and video, via your AV receiver, in multiple rooms in your house. For example: when watching a movie via Blu-ray in your living room, you can play music from a CD in your bedroom. Of course, both the Blu-ray player and CD player need to be connected to the receiver.
The number of channels determines how many speakers (in total) you can connect to your AV receiver. This also includes speakers you are planning to use in extra rooms, additional 'height' or 'width' speakers, and all 'bi-amp' compatible speakers. You can always decide to connect fewer speakers, but not more.