From the identd(1) manpage in Debian:
Identd is a server which implements the TCP/IP proposed standard IDENT user identification protocol as specified in the RFC 1413 document.

identd operates by looking up specific TCP/IP connections and returning the user name of the process owning the connection. It can optionally return other information instead of a user name.

In other words, if you have many users on your computer and one of them initiates a network socket to a remote host, identd lets the remote host know which user on your system did so. This permits the remote host's sysadmin to report or ban people by username@host rather than banning your whole host if one of your users does something stupid -- and, in other ways (as MrFurious points out below) take actions on the basis of username.

Why is identd important to you on a private workstation? Well, for the above reasons, many IRC servers and some FTP servers will refuse to accept a connection from you unless they can get user identification from identd on your system.