Dave Winer says A Full Peer is a computer that can be both a client and a server and is operating 24 hours a day 7 days a week. It can call other computers and can be called by other computers. A non-full-peer can't be a server - other computers can't call it. Usually it's a FireWall or a NAT that limits a computer in this way. Sometimes it's the ISP imposing the limit, or a corporate network. It's all the same - if you can receive incoming requests and process them your computer is a peer.
Mark Pilgrim doesn't like this idea. An default Windows 98 installation with a cable modem, visible on the Internet as a “full peer” (i.e. not firewalled or otherwise protected), will be found and hacked within minutes by automated script-kiddie-level scans. Not because it’s running a server of any kind, but because Windows clients are by default so insecure that they should never be visible on the public Internet... That, and running a publicly accessible server (which Radio is) probably violates your ISP’s terms of service for residential users. Lots of people got in trouble for (intentionally or not) running IIS servers last year when Code Red hit, and cable modem/DSL ISPs just started summarily disconnecting anyone running any kind of web servers, IIS or not.