You threaten all squares into which you can make a melee attack, even when it is not your turn. Generally, that means everything in all squares adjacent to your space (including diagonally). An enemy that takes certain actions while in a threatened square provokes an attack of opportunity from you. If you're unarmed, you don't normally threaten any squares and thus can't make attacks of opportunity.
Reach Weapons

Most creatures of Medium or smaller size have a reach of only 5 feet. This means that they can make melee attacks only against creatures up to 5 feet (1 square) away. However, Small and Medium creatures wielding reach weapons threaten more squares than a typical creature. In addition, most creatures larger than Medium have a natural reach of 10 feet or more.

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