A PC input, usually on a USB socket, will let the receiver carry the sound from your computer out through the speakers - handy if you have a lot of music and movies stored on the home computer.
Networking will allow the receiver to stream music from your PC or any network attached storage when the receiver is connected to a home computer network, as you might have if you have an ADSL or cable broadband service connected to your PC via a router. This also allows you to stream internet radio stations through the receiver.
Most receivers offering this function do this via an Ethernet/Cat5 wired network, but one or two are appearing with wireless networking built-in.
If you have a wireless network and a receiver that only 'does' wired Ethernet, you can buy a wireless device called an Ethernet bridge to interface between the network and the receiver, or use a powerline Ethernet system, which carries data on your home mains cabling, to create the link between the router and the receiver.
There's no difference between the two descriptions of a receiver you mention AV, home cinema and home theatre/theater are different terms for the same thing - the last, home theater, is an Americanism, as they have movie theaters, not cinemas!