Kaninen sover i sin kurv, mens hamsteren løber rundt i sit bur.

The ending -en is the usual way to make many Danish common-gender nouns definite singular, meaning the ....

• kanin = a rabbit
• kaninen = the rabbit
• hamster = a hamster
• hamsteren = the hamster

Unlike English, Danish often adds the definite article to the end of the noun instead of putting a separate word before it.

Because sin/sit means his/her/its own, and the form changes to match the gender of the noun being owned.

• kurv is common gender, so you use sin
• bur is neuter, so you use sit

So:

• sin kurv = its own basket
• sit bur = its own cage

This does not depend on the animal’s sex. It depends on the grammatical gender of kurv and bur.

Sin/sit/sine is a reflexive possessive. It refers back to the subject of the same clause.

In this sentence:

• Kaninen sover i sin kurv = the rabbit is sleeping in its own basket
• hamsteren løber rundt i sit bur = the hamster is running around in its own cage

If you used dens instead, it would usually mean the basket/cage belongs to something else, not the subject itself.

For example:

• Kaninen sover i dens kurv would suggest the basket belongs to some other animal or thing, not to the rabbit itself.

So in your sentence, sin and sit are exactly what Danish normally uses.

Mens means while. It connects two actions happening at the same time.

So:

• Kaninen sover i sin kurv, mens hamsteren løber rundt i sit bur means
• The rabbit is sleeping in its basket, while the hamster is running around in its cage

It is a very common conjunction for simultaneous actions.

Because Danish normally uses a comma before a subordinate clause, and mens introduces one.

So the structure is:

• main clause: Kaninen sover i sin kurv
• subordinate clause: mens hamsteren løber rundt i sit bur

In modern Danish punctuation, this comma is standard.

Løber rundt means runs around. The word rundt adds the idea of movement in circles, back and forth, or generally around within an area.

• løber = runs
• løber rundt = runs around

So hamsteren løber rundt i sit bur means the hamster is moving around inside its cage, not just running in one direction.

I usually means in.

Here it is used with places or spaces something is inside:

• i sin kurv = in its basket
• i sit bur = in its cage

That makes sense because both the basket and the cage are spaces the animals are located in.

Because Danish often puts the definite article at the end of the noun instead of using a separate word.

Compare:

• English: the rabbit

• Danish: kaninen

• English: the hamster
• Danish: hamsteren

This is one of the biggest structural differences English speakers notice early on.

They are both in the present tense.

• sover = sleeps / is sleeping
• løber = runs / is running

Danish present tense often covers both the simple present and the present progressive meanings that English separates.

So:

• Kaninen sover can mean The rabbit sleeps or The rabbit is sleeping
• hamsteren løber rundt can mean the hamster runs around or the hamster is running around

The context tells you which English translation sounds most natural.

After mens, Danish usually keeps normal clause order here:

• hamsteren = subject
• løber = verb
• rundt = adverb/particle
• i sit bur = prepositional phrase

So:

• mens hamsteren løber rundt i sit bur

This is a very natural word order in Danish. English speakers sometimes expect more inversion, but there is none here.

Yes, both are nouns:

• en kurv = a basket
• et bur = a cage

Their gender must usually be learned with the noun:

• kurv is common gender → en kurv, kurven, sin kurv
• bur is neuter → et bur, buret, sit bur

A good habit is to memorize Danish nouns together with en or et, not by themselves.

Yes, you could, but it means something slightly different.

• i sin kurv = in its own basket
• i kurven = in the basket

I sin kurv emphasizes ownership or belonging. I kurven just identifies the basket as definite, without explicitly saying it is the rabbit’s own basket.

In many contexts both are possible, but sin/sit is clearer when you want to show that the basket or cage belongs to the subject.