Level III refers to the NIJ specification for armor that can protect from rifle rounds up to 7.62mm NATO Full Metal Jackets. This is exclusively hard plate armor.
For the overwhelming number of situations NIJ Level III is enough. Short of high-caliber high-velocity or anti-material carbines it will protect from most anti-personnel weapons.
NIJ Level III is certified to stop at least 6 rounds of 7.62mm FMJ from a military issue rifle. It will also stop all fire from a .308 Winchester, .223 Remington, as well as 7.62×39 and 5.45×39 Steel Core rounds.