"He sleeps on Sundays."
Translation:Han sover om søndagen.
It is søndage. But you would never say "han sover om søndage" in danish. "Søndage sover han" is possible but mostly as a reply to a question
It is a bit like "I drink coffee in the morning" can be about more then one morning even though morning is singular
I think what changes the meaning in danish is "om" had it been på søndag it would.be next sunday.
I hope this helped
It's a statement about the time of a general day. It is indeed quite common in English too, here's another example: "In summer many people go to the beach". Of course there is not just one summer, it is summer every year. But for every year it applies that in that summer many people go to the beach, so as a general statement you can say "in summer".