Zeroconf is a technology to access network resources such as computers, printers, etc. without knowing their IP addresses.

For example, to access the web server running on the computer named blacktower on your local area network (LAN), just type blacktower.local on your browser.

To download files from Andrew's laptop, just type andrew.local on your FTP client.

You may find more information about zeroconf from Apple's Bonjour.