A tooltip is a small window that pops up when you hover your mouse over certain UI elements (other characters, mobs, items, buttons, etc.) displaying a description of the element or item. This also works in many other computer programs. For example, hold your mouse over the "wikia" logo image ( ← this one should show "This is a tooltip") in the upper-left, and a small box saying "Wikia" will appear (usualy down and to the right, but position may vary).
This term comes from general computer UI tool tips from buttons or icons.
In World of Warcraft
Items that have tooltips will appear in their quality color text and have square brackets () around their name. Achievements, abilities, quests, and spells will have square brackets, but will have a different color that doesn't correspond to quality (usually slate blue or yellow).
Many aspects of WoWWiki will also show tooltips. Some will have square brackets (), but some won't (battle pets, mobs, NPCs, quests, etc.)
See Help:Tooltips for information about how to make tooltips work on special links in WoWWiki.