Wikipedia
Gezelligheid is a Dutch abstract noun (adjective form gezellig) which, depending on context, can be translated as convivial, cosy, fun, or nice atmosphere, but can also connote belonging, time spent with loved ones, the fact of seeing a friend after a long absence, or general togetherness that gives a warm feeling.
The only common trait to all descriptions of gezelligheid is a rather general and abstract sensation of individual well-being that one typically shares with others. All descriptions involve a positive atmosphere, flow or vibe that colors the individual personal experience in a favorable way and in one way or another corresponds to social contexts.
As this is a very vague and abstract notion, the word is considered to be an example of untranslatability, and is one of the hardest words to translate to English. Some consider the word to encompass the heart of Dutch culture.