It means "coziness" or "contentedness" or the feeling you feel when you feel just at home. According to Wikipedia, "Gemütlichkeit connotes the notion of belonging, social acceptance, cheerfulness, the absence of anything hectic and the opportunity to spend quality time."
Today, I was talking with a fellow American (David)- he said this is what his grandfather called it when David at sixteen visiting England, felt a strong sense of belonging and peace and felt Europe was one day where he'd end up.
I thought, the perfect word, Gemütlichkeit. The perfect description. I remember feeling like that when I came over here in 1995 with the Jones cousins. It only heightened when I spent two months over here with a now ex-boyfriend in 2001. I always wanted to come back and live here but I thought I'd never be able to do it as an optometrist.
So here I am.
Living Gemütlichkeit. It is good.