What does it mean? 

Gratuler med dagen means “congratulations with the day” when translated very literally. Grammar-wise, it is worth noting the er at the end of the word makes it plural, and the en on dagen makes it “the day”. 

Many will simply shorten this to gratulerer (congratulations). Essentially, the expression is used to express your well wishes on somebody’s important day. 

The expression can be used for birthdays, weddings, christening, graduations. Norwegians will also say it to one another on May 17th, Norway’s “national day”. 

There are some nuances, so you would say it on a wedding day rather than an anniversary. For an anniversary it’s best to commemorate the day with a “gratulerer med bryllupsdagen” (happy anniversary). 

You also wouldn’t use it for a colleague getting a promotion, in that case gratulerer would be a lot more suitable. 

When using gratulerer med dagen for a birthday, it could be compared to the English expression “many happy returns”.