First of all, hygge means nice or cozy or comfort in everyday speech.
“Hyggeligt” to meet you, this is “hyggeligt”, and “hyg dig” which means “have a good time”.
But as a phenomenon “hygge” means creating a place and situation that keeps the uncomfortable, cold and formal world out. Soft clothes, hot beverages, candles and low pleasant music, with a good book or informal conversation, pretending time doesn’t exist.
Many objects can be “hygge”, like “hygge-socks”, “hygge-food”, and “hygge-lights” – objects that strengthens the feeling of well-being and informality.
“Hygge” also means not trying to achieve anything. “Hygge-football”, for example, means playing football without actually keeping score, and being patient with someone leaving the field to have a sip of his beer.
“He is hyggelig” means he makes you feel at ease in his company.
A “hygge-evening” can be meeting to play board games with a nice glass of wine or a mug of hot cocoa, and plenty of pauses to talk.
For “hygge” you can’t talk politics or anything else that will make your blood boil. And you definitely can’t wear a tie. It has to be pleasant, informal, and gentle impressions. Soft clothes, soft light, soft conversation, unhealthy food (pastries, crisps and sweets), and no time-keeping.

Danes work hard and focused, multitask, plan everything in details, and are generally over-achievers. We are unfiltered opinionated and never shy away from a debate. We are cynically rational and efficient.
Hygge is the antidote, where we turn it all off.