A super bad hangover. Similarly to 'fugly' or the combination of 'fucking' and 'ugly'...'fungover' is the combination of 'fucking' and 'hungover. This shortened version takes out the extra word and thus reduces the amount of work it takes to express just how bad the morning after is.
"Holy shit I'm fungover."
"I'm so fungover I think I might die."
"Someone make me a sandwich, I'm so fungover I don't think I can move."