It is ostensibly for you to write memos relevant to the item; for instance, if you have a complicated item you could write out what it does in plain language - it will never appear in-game to the player, but it could help the game maker in remembering the purpose of things. Whenever you don't know what something is, just right-click and press "What's this?" when it comes up.
It also serves a useful function for custom scripts. A number of scripts that add stats to items, or states, or whatever allow you to use the notebox to indicate the values relevant to that script. Any scripts that do that will provide specific instructions on what needs to be written in the note box so there is no reason to elaborate further on that subject.
EDIT::
What Basch said.