Gryning means 'dawn'; the time of day when night comes to an end and the sun starts to rise.
It comes from the verb gry (to dawn), which is related to the adjective grå (grey), so it conveys the idea of going from a totally dark night to a lighter daytime, and a similar word exists in Norwegian: grålysning (literally 'grey lighting').
You can also use it metaphorically, as in English, to talk about the dawn of a new era or another kind of symbolic beginning.
Gryning is a popular word in Swedish, and is regularly called one of the language's most beautiful words.
Det är som mörkast innan gryningen
It is darkest before the dawn
It was dawn when she was on the way home