The vampiric trait (and subtype) heal for half the damage caused. Excess damage does not count for healing.
Pg 44 rulebook V2
Necro Vamp deals 5 regular damage (no crits) to an enemy with 3 armor so she only take 2 points of life (inflicts 2 would counters) on enemy. Does Necro Vamp heal 3 or 1?
She heals 1. Only 2 damage was caused / dealt as 3 was absorbed / canceled.
Cancel (pg 40 rulebook v2)
If a spell, attack, or effect is canceled, it stops and has no further effect.
To go further into armor:
Armor literally subtracts from the die roll when it is rolled not after. So lets look at your example again:
"
Necro Vamp deals 5 regular damage (no crits) to an enemy with 3 armor so she only take 2 points of life (inflicts 2 would counters) on enemy. Does Necro Vamp heal 3 or 1?"
The vamp rolls 5 - 3 armor for a total of 2 damage vampiric damage. She only caused 2, she never "causes" 5 because armor is factored into the roll and not compared to the roll.
I will add in the rulebook quote here
(Pg 25)
"First, add up the value of all critical hits showing on the attack dice. This damage ignores armor, so it is applied directly to the target. Then, add up the value of all normal hits showing and subtract the target's armor from this total. If the result is more than zero, that target also suffers that much damage."