SAY WHAT?
Let's deal with the elephant in the room, Danish is not a language that lends itself to easy utterance and hygge's deceptive spelling instils fear in many. It's simple really: hoo-guh.
LISTEN: How to pronounce hygge

SO, WHAT IS IT THEN?
First and foremost it's a philosophy, a Danish way of living that fosters happiness and is largely based on comfort.
It has no direct English translation, but aligns itself rather to a string of adjectives that closely describe it - cosiness, contentedness, simplicity, kinship and many more. It's also intangible - it's an atmosphere you create, a feeling you get, an acknowledgement of a special moment.
Alex Beauchamp of the blog hyggehouse.com puts it best: "Hygge is about being present enough to recognise and acknowledge an act, moment or feeling when the ordinary feels extraordinary."
Another term that came up in a search for hygge was: "how to actually enjoy winter", nodding to the doctrine's strong ties with the colder months...