Armor or body armor is used for protection against guns. It is like a second health, so you can endure more damage before you become wasted. When you are hit wearing armor, your armor will decrease first; your health will only decrease once you have run out of armor. Armor is only useful when being shot: other injuries like falling from great heights, punches or fire damage will directly decrease your health, even when wearing armor.
Armor has been available since the first Grand Theft Auto. Since the release of GTA III you are able to buy armor at any Ammu-Nation.