I smell what you did last night...
Maybe that after-work drink turned into two or three. It's easy to lose track, when you're having fun with friends. Or maybe you were out celebrating your birthday until the wee hours of morning. At any rate, if you were drinking alcohol, you'll probably have a headache - and a "Fahne" - the next morning.
A "Fahne" is the unwanted result after drinking numerous cocktails, beers or glasses of wine. It is the resulting odor of alcohol in your breath, generally the next day. Although it literally means, "flag," in German, the word "Fahne" in this context is more like a flag of bad breath waving in front of one's mouth.
It's not a good thing if someone says, "You have a Fahne today!" because if you "have a Fahne," that means your breath smells of alcohol. Although the most typical "Fahne" to have is an alcohol "Fahne," it is also possible to have a garlic "Fahne," or "Knoblauchfahne." In either case, it might be helpful to have some breath mints handy.