Unarmed Strike
An Unarmed Strike is a special attack involving a character's fists, elbows, feet, head, knees, or any part of his body. The Simple Weapon Proficiency feat does make a character proficient with this attack, but they Present an Opening when they attack. Additionally, their unarmed attacks deal sublethal damage, instead of lethal. In addition, without this feat striking with anything other than the fists takes a -2.
Unarmed strikes are never an Off-Hand Weapon, so you never take penalties when attacking with them when using other weapons. You can strike even if your hands are full, with feet, elbows, knees, or even other parts of your body.
In order to bypass these two restrictions, a character must purchase the Improved Unarmed Strike feat. With that feat, a character no longer Presents an Opening when attacking with an unarmed strike, and the attack deals lethal bludgeoning damage.
Fighting unarmed without training gives you a -2 to AC, but Improved Unarmed Strike and Brawler both reduce it to a -1. Empty Hands eliminates the AC penalty altogether.