Translation:They are visiting the grandmother and the grandfather.
In English the possessive is used a lot more than in some languages, such as Spanish, for example. If someone asks where the children are, for example, it would be very common for us to say "Están con el abuelo" (they are with the grandfather...i.e. their grandfather) The possessive is implied, which is fine. In English though we almost always say with THEIR grandfather, as the possessive is not implied, at least where I live. If someone days "they are visiting the grandfather" the first thing that comes to mind is "they are visiting the grandfather? WHOSE grandfather exactly are they visiting?
I assume from the abundance of sentences like that that, like in Spanish Portuguese, and so many other languages, that the possessive is also implied in Dansk, thus although the literal translation is "They are visiting the grandmother and the grandfather" the meaning is implied that they are in fact visiting their (own) grandparents. Am I correct in making that assumption?
From what I read here in many exercises, your assumption appears to be correct. Also, as a German, I can confirm your assumption for the German language, which has many similarities to Danish.
I'd say that is only the case in Southern Germany. When I moved to the South (from Bremen) I'd often here people talk about "die Frau" which to me sounded like either there was a woman in Southern Germany who was so great/well-known that she was just THE woman or much rather it sounded to me like a very derogatory term for SOMEONE'S wife.
I am from the West of Germany (Niederrhein = Lower Rhine Region, North Rhine-Westphalia). There, it is very common to use a definite article instead of a possessive pronoun: Morgen gehe ich mit der Frau essen = Tomorrow, I will go out for dinner with my wife. This also applies to the Ruhr area. There is nothing derogatory with that. Some people even say that "meine Frau = my wife" is somehow derogatory because she is not my own.
The singular form is quite rare, though. The plural form is common: bedsteforældre