På den samme bænk sad en pige og så på en due, mens et egern løb op i træet.

Because Danish is a V2 language: in a main clause, the finite verb usually comes in the second position.

If you start the sentence with the place phrase På den samme bænk, the verb sad must come next, and the subject en pige comes after it:

• En pige sad på den samme bænk
• På den samme bænk sad en pige

Both are grammatical, but the second version gives extra focus to the location, a bit like On that same bench sat a girl in literary English.

This is the normal Danish pattern for a definite noun with an adjective:

• den/det/de
  • adjective + noun

So:

• en bænk = a bench
• bænken = the bench
• den samme bænk = the same bench

When there is an adjective like samme, Danish usually uses a separate definite article before the adjective: den for common gender, det for neuter, de for plural.

Samme is a special word meaning same, and it does not really change form here the way many ordinary adjectives do.

So you get:

• den samme bænk
• det samme træ
• de samme mennesker

For a learner, it is easiest to remember samme as a fixed form.

Sad is the past tense of sidde.

It means sat / was sitting.

So en pige sad means the girl was already in a sitting position. It does not mean sat down. If Danish wanted to express the action of sitting down, it would use a different verb, often sætte sig.

Here så på is best understood as looked at / was watching.

This is based on the verb se på, which means look at.

So:

• så by itself can mean saw
• så på means looked at / watched

That is why en pige og så på en due means the girl sat and looked at a pigeon, not that there were two separate past-tense verbs with unrelated meanings.

Because Danish, like English, can join two actions with og when they have the same subject.

So:

• En pige sad og så på en due

means:

• A girl sat and looked at a pigeon

The subject en pige applies to both verbs:

• sad
• så på

This is very common in Danish.

Mens means while.

It introduces a clause that describes something happening at the same time:

• mens et egern løb op i træet = while a squirrel ran up into the tree

So the sentence presents two simultaneous actions:

1. the girl was sitting and looking at the pigeon
2. the squirrel was running up the tree

Because mens introduces a subordinate clause.

In Danish subordinate clauses, you do not get the same V2 inversion pattern as in main clauses. So the basic order is simply:

• conjunction + subject + verb

Here:

• mens
  • et egern
    • løb

That is why mens et egern løb op i træet is normal.

Because Danish nouns have grammatical gender.

There are two genders in modern Danish:

• common gender → usually takes en
• neuter → takes et

In this sentence:

• en pige = a girl
• en due = a pigeon
• en bænk = a bench
• et egern = a squirrel

Unfortunately, gender often just has to be learned with each noun.

Træet is the definite singular form of træ:

• et træ = a tree
• træet = the tree

So op i træet means up into the tree / up the tree.

Danish uses the definite form here because the tree is treated as a specific tree in the scene.

Op i expresses movement upward into a higher position.

So løb op i træet means the squirrel ran up into the tree or more naturally in English, ran up the tree.

Danish often uses combinations like this:

• op = up
• i = in/into

Together they describe upward movement to a location.

Because mens et egern løb op i træet is a subordinate clause, and Danish commonly separates such clauses with a comma.

So the comma marks the boundary between:

• the main clause: På den samme bænk sad en pige og så på en due
• the subordinate clause: mens et egern løb op i træet

This kind of comma is very common in written Danish.