Det er min søster, der læser flest bøger i familien.

This is a very common Danish pattern called a cleft sentence:

Det er X, der ...

It is used to highlight or focus on one part of the sentence.
So:

Det er min søster, der læser flest bøger i familien.

means something like:

It is my sister who reads the most books in the family.

The point is not just to state a fact, but to emphasize my sister as the person being identified.

A more neutral sentence would be:

Min søster læser flest bøger i familien.

That means basically the same thing, but with less emphasis.

In this structure, det does not mean that your sister is an it.
Instead, det is part of the fixed pattern Det er ... der ....

You can think of it as similar to English:

It is my sister who ...

In English, it also does not refer to an object here. It is just part of the sentence structure used for emphasis.

So in Danish, det is structural, not literal.

Here, der means who/that in the sense of a relative pronoun.

So:

min søster, der læser flest bøger
= my sister, who reads the most books

In this sentence, der introduces the clause that tells us something about min søster.

So the structure is:

• Det er min søster = It is my sister
• der læser flest bøger i familien = who reads the most books in the family

In Danish, der is normally used when the relative pronoun is the subject of the relative clause.

Here, in:

der læser flest bøger i familien

the word der stands for min søster, and min søster is the one doing the reading. That makes it the subject of the clause.

So der is the standard choice.

Very roughly:

• der = who/that, when it is the subject
• som = who/which/that, often in other relative-clause situations

In cleft sentences like this one, der is especially standard:

Det er min søster, der ...

In Danish, possessives like min, din, hans, vores normally come directly before the noun without a separate definite ending.

So:

• min søster = my sister
• din bog = your book
• vores bil = our car

You do not say:

• min søsteren
• din bogen
• vores bilen

The possessive already makes the noun definite enough, so Danish does not add the definite ending here.

læser is the present tense of at læse = to read.

So:

• at læse = to read
• læser = read/reads

In Danish, the present tense usually ends in -r, and it does not change depending on the subject.

So you get:

• jeg læser = I read / I am reading
• du læser = you read
• han læser = he reads
• min søster læser = my sister reads

Unlike English, Danish does not have a special -s form only for he/she/it. The same present-tense form is used for all persons.

flest is the superlative form of mange = many.

The forms are:

• mange = many
• flere = more
• flest = most

So:

• mange bøger = many books
• flere bøger = more books
• flest bøger = most books

In this sentence, læser flest bøger means:

reads more books than anyone else in the family

So the sentence says your sister is the family member who reads the highest number of books.

This is an important distinction.

• flest bøger = the greatest number of books / most books
• de fleste bøger = most of the books

In your sentence, the meaning is about quantity read by a person in comparison with other people:

She reads the most books.

That is why Danish uses flest bøger.

If you said de fleste bøger, it would usually refer to the majority of the books themselves, not the highest number read by one person.

Compare:

• Hun læser flest bøger i familien.
  = She reads the most books in the family.

• Hun har læst de fleste bøger på listen.
  = She has read most of the books on the list.

Because Danish, like English, often uses a bare plural after words like many, more, and most.

So:

• mange bøger = many books
• flere bøger = more books
• flest bøger = most books

You do not need an article here.

Also, bøger is just the plural of bog:

• en bog = a book
• bogen = the book
• bøger = books
• bøgerne = the books

i familien means in the family.

Here Danish uses the definite form familien, because it refers to a specific family: the family being discussed.

This is very natural in Danish in expressions like:

• i familien = in the family
• i klassen = in the class
• på holdet = on the team

Even though English sometimes says in my family, Danish can often simply say i familien when the context already makes it clear whose family is meant.

You could also say:

i min familie

which also means in my family, but i familien is very idiomatic here.

Yes, in a way.

After der, the clause has the normal order of a subordinate clause:

der læser flest bøger i familien

Here the subject is understood through der (= my sister), and then the verb comes in its normal place.

This is different from main-clause word order in Danish, where the verb often appears in second position.

Compare:

• Min søster læser flest bøger i familien.
  Main clause

• Det er min søster, der læser flest bøger i familien.
  Cleft sentence with relative clause

So yes, the second part is grammatically a different kind of clause.

Yes, absolutely.

That is a completely natural sentence and means essentially the same thing:

My sister reads the most books in the family.

The difference is mainly focus:

• Min søster læser flest bøger i familien.
  More neutral statement.

• Det er min søster, der læser flest bøger i familien.
  More emphatic: It is my sister who reads the most books.

So the original sentence is especially useful when you want to identify or contrast the person.

Just compared with the family members.

The phrase i familien limits the comparison. So the meaning is:

Among the people in the family, my sister is the one who reads the most books.

Without i familien, the sentence would be much broader and could sound incomplete unless the context made the comparison clear.

Yes, very often.

Because of the Det er ... der ... structure, the sentence can easily sound contrastive:

Det er min søster, der læser flest bøger i familien.

This may suggest something like:

• not my brother
• not me
• not my mother

but my sister

Whether that contrast is strongly felt depends on the context and intonation, but the structure is often used exactly for that kind of emphasis.

The biggest thing is that Danish and English use very similar structures here, but not always in exactly the same way.

A close translation is:

It is my sister who reads the most books in the family.

But in normal English, people might also simply say:

My sister reads the most books in the family.

So if you translate word-for-word, the result is fine, but remember that the Danish version may sound slightly more naturally emphatic than the most common English phrasing.