The period following any surgical procedure (involving general anesthesia) where one feels like absolute crap for a duration of time. For most shorter procedures, this period can literally be mere hours. The hangover includes both the time in the recovery room, as well as the complete recovery back to how you felt prior to surgery.
For longer, more complicated procedures however, that period can take several days before you start feeling like a human being again.
As with traditional hangovers, when you're having the surgical variety, you tend to feel not unlike death warmed over.
I had a 5 hour brain surgery the other day and I'm still feeling the hell. I swear, I have a major surgical hangover!