There's unarmed strikes and natural attacks. The two are different. What the monk gets is a class ability called "unarmed strike" and a class ability called "flurry of blows". The "flurry of blows" lets her, as a full-attack action, make an additional attack at her base attack bonus using either unarmed strikes or weapons with the "monk" special quality (that is labeled in the weapon description), or a combination of the two. The "unarmed strike" piece of that is a general game mechanic term that applies to any body part--so if the monk's hands are tied, they can still unarmed strike by kicking or head-butting or whatever. The exact body part used isn't specified, but all are subsumed under the term "unarmed strike".
Natural attacks, in game terms, are a different beast (pun intended), and not something you have to worry about for a monk.
WITH THE EXCEPTION that spells that target natural weapons (like magic fang) treat the monk's unarmed strike as a natural weapon while spells that target manufactured weapons (like magic weapon) ALSO can affect the monk's unarmed strike. You (usually) don't have to worry about body-part specifics for such spells--unless your GM really wants you to.
Unarmed Strikes aren't Natural Attacks.
A human monk has no natural attacks (same for most humanoid races).