Kunden kniber øjnene sammen, mens hun læser synstavlen.

Because kunden means the customer.

In Danish, nouns often add -en or -et to show definiteness, instead of using a separate word like the.

• en kunde = a customer
• kunden = the customer

So kunde is the basic noun, and kunden is the definite singular form.

Because øjnene means the eyes.

Here is the pattern:

• et øje = an eye
• øjne = eyes
• øjnene = the eyes

Danish often uses the definite form for body parts where English might use a possessive:

• Danish: hun kniber øjnene sammen
• Natural English: she squints her eyes or more simply she squints

So øjnene is definite plural.

Because Danish very often uses the definite form of body parts when it is already obvious whose body part is meant.

So instead of saying her eyes, Danish naturally says the eyes:

• Hun vasker hænderne = literally She washes the hands, meaning She washes her hands
• Han løfter armen = literally He raises the arm, meaning He raises his arm

In your sentence, hun is the person reading, so it is already clear whose eyes are being squeezed together.

It is a fixed expression meaning to squint or to narrow one’s eyes.

Literally:

• kniber = pinches / squeezes
• øjnene = the eyes
• sammen = together

But in natural English, the whole phrase means something like:

• The customer squints
• The customer narrows her eyes
• The customer screws up her eyes

So this is a good example where the literal meaning and the natural meaning are a bit different.

Sammen means together, but in this expression it helps create the meaning squeeze together / narrow.

In knibe øjnene sammen, it is part of the idiomatic phrase. Without sammen, the sentence would feel incomplete or at least less natural for this meaning.

So it is best to learn knibe øjnene sammen as one unit.

Both are present tense verbs.

• kniber = squints / is squinting
• læser = reads / is reading

Danish present tense is often used both for:

• habitual actions: she reads
• actions happening right now: she is reading

So in this sentence, the present tense describes what is happening in the moment.

Yes. The sentence contains:

1. a main clause: Kunden kniber øjnene sammen
2. a subordinate clause introduced by mens: mens hun læser synstavlen

In the main clause, the normal order is:

• subject + verb
• Kunden kniber

In the subordinate clause, Danish also keeps:

• subject + verb
• hun læser

So in this particular sentence, both clauses look similar. The important thing is that mens introduces a subordinate clause meaning while.

Mens means while.

It connects two actions that happen at the same time:

• Kunden kniber øjnene sammen
• hun læser synstavlen

Together: The customer squints while she reads the eye chart.

A useful thing to remember is that mens introduces a subordinate clause.

Yes.

You can say:

• Mens hun læser synstavlen, kniber kunden øjnene sammen.

When the subordinate clause comes first, the main clause usually has inversion:

• kniber kunden not
• kunden kniber

That is a very common Danish word order pattern.

Synstavlen means the eye chart.

It is made up of:

• syn = vision / sight
• tavle = board / chart
• synstavle = eye chart
• synstavlen = the eye chart

So again, the -en ending marks the definite form.

Yes, it could be han if the customer were male.

Danish nouns like kunde are not grammatically female or male in the way some languages do it. Kunde just means customer. The pronoun depends on the actual person being referred to.

So:

• Kunden ... mens hun læser ... = the customer is female
• Kunden ... mens han læser ... = the customer is male

Those are two sounds English speakers often find difficult.

In this sentence:

• ø appears in øjnene
• y appears in synstavlen

A rough guide:

• ø is a rounded front vowel. English does not really have an exact equivalent. You make a sound somewhat like e in bird or i in sir, but with rounded lips.
• y is also rounded, a bit like saying ee while rounding your lips.

You usually need to hear these from native audio to get them right, because English does not match them closely.

Yes in meaning, but not in form. Læser is the present tense of læse, which means to read.

The forms are:

• at læse = to read
• læser = reads / is reading
• læste = read (past)
• har læst = has read

So if you know læse, then læser is just the present tense form.

It is natural Danish.

A native speaker would understand it immediately, and the phrasing is normal:

• Kunden = definite subject, natural in context
• kniber øjnene sammen = normal expression for squinting
• mens hun læser synstavlen = natural way to say while she reads the eye chart

So this is a good example sentence to learn from.