ZeroConf, sometimes called Rendezvous, provides a means to search the local IP subnet for resources. For example if you want to find a printer: you broadcast via multicast from your machine a request for anybody on the local subnet who has a printer. Machines with resources to offer listen for such requests and reply when appropriate.
For example in my workplace people running iTunes offer their music collections for other folks to listen to. My iTunes, acting as a client, broadcasts a request for music servers. (These uses something called daap, or Digital Audio Access Protocol) These requests take place via something known as mDNS, or multicast DNS. On the machines of my generous coworkers an mDNS notices my request and replies with the IP address and port number where their daap server is listening. That