Body armor will extend your normal health meter, and provide you with additional support. GoldenEye 007, by itself, does not feature any medic-kit pick-ups, and therefore, getting hit without the Body Armor will stay with Bond until he finishes the mission and presumably gets healed afterwards. Bond must therefore for special armor vests, to protect himself from damage, as it can later be refilled by more armor.
By a glitch, if the armor is shot with a weapon while it's in its pick-up state (in fact only one shot), it can no longer be picked-up and will be destroyed.
For quite some time now, it has been assumed that there was supposed to be a final cheat in the cheat-menu, because it seemed like it was missing one cheat. The hoax would be called "Dr. No", and would an absolutely unneeded effect of "disabling", thus making the Solo and Multi levels harder.