It doesn't really, not if you start thinking about it. Poisons in real life are incapacitating, if you are poisoned with enough of a dose to affect your performance you are not going to be dancing about sword fighting. Gary was absolutely correct in that one, they are save or suck and you die with out pretty specific treatments or you just die outright with out some immediate and particular intervention.
However, none of that is much fun in a game sense, so WoTC replaced those effects with hit point damage and the poisoned condition.
Hit points are a gamest structure to make fights fun. It is a form of plot protection.
I mean, what is Armor Class? In the real world you are not harder to hit if you are wearing full plate as against stark naked. You are about the same difficulty to hit but the hit is vastly less likely to do damage if you are armoured.
There is a one to one correspondence between a defence value against an enemy attack roll for a wargame unit and AC vs the hit roll in D&D as there is a one to one correspondence between figures lost from the unit (in a minis battle) and hit points.