"German Gemütlichkeit" is a stereotype among overseas visitors, especially Americans, that most Germans consider a bit of a laugh.
"Gemütlich" is a term that no German would attribute to, for example, a beer hall or an Oktoberfest tent. It means quiet, cosy surroundings where one feels relaxed, at ease, "at home". Think a cuddly sofa you never want to rise from, candles on the table, a good wine in your glass, the cat purring in your lap, friendly company to talk to... that's what we'd call "gemütlich".