Blood Drain isn't actually an official MTG keyword—you won't find it in the comprehensive rules. It's likely a casual nickname or a mix-up with similar effects. The closest real mechanics are "lifelink" (damage dealt also gains you that much life) and "drain" effects, which combine dealing damage or making an opponent lose life with you gaining the same amount.
A common point of confusion: lifelink isn't a triggered ability—life gain happens simultaneously with the damage, so you can't respond between them. By contrast, a card like Gray Merchant of Asphodel "drains" by making opponents lose life and you gain it as part of a resolving spell or trigger, which is a separate, often counterable event.
In Commander, drain effects shine because they scale across multiple opponents—Gary draining a four-player table can swing 20+ life. If you meant a specific card, double-check its exact Oracle text.