Dark Lord on Life Support is an event that has left a very powerful wrongdoer severely injured or drained of power, and so, his minions hook him up to a device that will keep him alive for the time being, and such means of survival does not have to be a machine; it can be the inability to survive without attaching to another body.
This can be a way of creating sympathy for the villain by showing that he is weak or dependent. The weakness can be exploited by someone attacking him or her. The evil overlord may not have full strength because of what has happened to him or her, or may be stuck in one place.
Dependence means that the hero can destroy the support system to destroy his enemy (although there might be moral issues with dealing the killing blow to a villain who can't fight back).
Frequently, the very thing that made a Dark Lord this way was done by the hero, sometimes in a battle that did not succeed in completely killing the villain. This can be a sign that the hero was never ready to fight the villain, that he did so rashly, etc. Alternately, the dark lord may have been left in this state by the hero of a previous generation, rather than the protagonist.
Sometimes the Dark Lord's weakened state is caused by age or disease rather than combat injuries. In such cases, the life support usually indicates an obsessive fear of death or desire for immortality.
NOTE: It is possible for a said Dark Lord to recover from this, maybe even come back stronger than ever.
Aesthetically, this trope associates the villain with illness and death, which in turn makes him seem creepier than he would be otherwise.