When you hover your mouse over certain items (other characters, mobs, items, buttons, etc.) a small window will pop up displaying a description of the item. This also works in many other computer programs. For example, hold your mouse over the "W" logo image ( ← this one should show "This is a tooltip") in the upper-left, and a small box saying "Portal:Main" will appear.
This term comes from general computer UI tool tips from buttons or icons.
See Help:Tooltips for information about how to make tooltips work on special links in WoWWiki.