NickServ maintains a list of nicknames that you have identified to. The unidentify command allows you to remove an entry from that list, effectively making NickServ unaware of the fact that you have identified to that nick.
Example:
/msg nickserv unidentify NikB
This is useful if you wish to not have access to the abilities that go with that nickname. For example, if you identified to a nick that is an AOP in a room, but you wish to enter without being opped, you can unidentify. It is also useful if you want to unidentify from your network operator nick, so that you no longer have CSop access. You can, of course, get your access back simply by identifying. If you wanted to let someone else use your computer, you would probably want to unidentify to all of your nicks and rooms, de-oper, and switch nicks.