It’s pretty safe to say it is not based on reality.

It’s meant to weaken the character like, you know, how losing blood to a vampire might make you weaker.

It was there in the original versions of D&D. It also exists in Rogue, etc.

Like many things in D&D, it’s has pretty weird, sloppy, gamey mechanics, in my opinion. Levels in D&D are gained with experience points, which often come from weird things other than experience, such as how much gold you take. Thinking literally about many (most?) things in D&D tends to lead to silliness and contradictions, it seems to me, which is why I always preferred more logical games.

Experience is one of the prized accomplishments of players, and losing levels means losing a lot of play rewards, so it makes vampires particularly “scary” for players, especially players who get upset when their characters lose things (and many D&D players, particularly in later generations, really hate to lose things…). In comparison to conventional weapon attacks in D&D, losing levels not something that can be easily and quickly restored, while physical damage generally is very recoverable with little or no consequence, so that also adds to the fear and loathing.

I don’t know that there is a good consistent explanation of what the level draining is supposed to represent in D&D, as levels are an artificial game mechanic and not a real-world thing, per se. Some people and different versions may have more or less, and different opinions. See for example this post wondering the same sorts of things: http://grognardia.blogspot.com/2010/05/energy-drain.html which invites and receives opinions from others in comments.

Real-world vampire lore also varies quite a bit from version to version. However it is pretty common that the sucking of blood leads to a condition or disease often called vampirism, which includes lack of energy and willpower (particularly against vampiric suggestions) and often conversion into a minor vampire oneself. So it would be reasonable to think that in D&D it involves blood sucking and the effects of both blood loss and the disease and/or vampiric magic, though depending on how you imagine D&D’s abstract combat, it might be a magic ability that doesn’t need to literally mean sucking blood through a bite.

In pop psychology, there is the term “emotional vampire” which does describe people who such the life from others, generally by means of asocial passive behaviors.

It is worth noting that such draining is pretty much limited to D&D and “Roguelikes”. Other gaming systems don’t really have the consequences of a fight with a vampire last too long; you either heal the HP you lost in the fight and go on with your life, or you get killed and turned; there is no sort of “level drain” that causes permanent impairment for a fight that didn’t kill you outright.

Of course, D&D’s biggest fault is probably it’s class/level-base system. While in other games your power level is determined by your skills (which you can learn without artificial restrictions), D&D uses “Level” as an uber-stat to determine ALL of your abilities. Comapred to level, nothing else really matters. Therefore, the only thing many players feel truly threatened by is losing levels. The end result is that the only thing that can really scare a player is level-draining, and since vampires are supposed to be scary, they are given the ability to drain levels.