I think it's best put this way: Armor:2 should mean that a direct hit from something Weapon:2 that would have killed instead means you only take a stress hit, yes? Where the weapon rating itself is the cause of an attack going past the stress track.
So by this definition, let's call a direct hit a hit that would have landed the stress on the target's last stressbox before taking into account the weapon rating--all of the weapon rating, therefore, is past the stress track and would normally result in a kill.
So your average vest available is Armor:1--it reduces the lethality, but on a direct hit it's still going to hurt.
A reinforced vest--the kind of thing your average SWAT team or military commandos will be wearing--is stronger. A direct hit from small arms will, for the most part, be shrugged off. It's Armor:2 because it completely protects from the force of the bullet--you'll feel it, but it won't hurt you. Heavier weapons--automatic rifles, shotguns--will still hurt, however.
Highly advanced body armor--think Dragonskin, maybe, or bomb disposal suits--are rated to protect against stronger weapons, so are overkill against small arms. They're Weapon:3, so on a direct hit, the character is protected such that it's less effective than a normal punch would've been, and it can therefore take more punishment.
Armor:4, as the books point out, just isn't something you get on a personal scale. Here we're talking about the kind of armor where you could lay on a grenade and expect not only to survive, but get up again pretty much right away.
For melee, Armor:1 is probably things like leather armor--it provides some protection against small knives which are being used with little force, but protection is limited against anything bigger.
Armor:2 is going to be heavier chainmail over leather--you need metal to stop someone swinging a sword, but at the same time they're still swinging a sword. It might prevent cuts, but it's not going to stop the force of the blow, only absorb and mitigate it some.
Armor:3 would be full-body plate mail--able to simply shrug off blows from swords without injuring the person underneath.