Jo flere bøger jeg læser, jo bedre forstår jeg teksten.

It creates the Danish pattern for the more ..., the better ....

So the structure is:

jo + comparative ..., jo + comparative ...

You will see this in many similar sentences, for example:

• Jo mere jeg øver mig, jo bedre bliver jeg.
• Jo tidligere du kommer, jo bedre.

It expresses a relationship where one thing increases or changes together with another.

It is the same word in spelling, but not the same function.

Danish jo can have several uses:

• jo = yes when replying to a negative statement or question
• jo as a modal particle, something like after all or of course
• jo in the pattern jo ..., jo ...

In your sentence, it is the third use. It does not mean yes here.

Because bøger is a countable plural noun.

Use:

• flere with countable plural nouns: flere bøger, flere mennesker, flere biler
• mere with uncountable nouns or with a more general idea: mere vand, mere tid, mere arbejde

So:

• Jo flere bøger jeg læser ... = the more books I read
• Jo mere jeg læser ... = the more I read

Both are correct, but they mean slightly different things.

Bedre means better. It is the comparative form of god/godt.

It can be used both:

• as an adjective: en bedre idé
• as an adverb: jeg forstår det bedre

In this sentence, it works adverbially, because it describes how well the text is understood.

Because the second half is a main clause, and Danish main clauses normally follow the verb-second rule.

That means if something else comes first, the finite verb comes next.

Here, jo bedre is placed first, so the verb must come right after it:

• jo bedre forstår jeg teksten

Compare the normal word order:

• Jeg forstår teksten bedre.

When bedre is fronted, Danish changes the order:

• Bedre forstår jeg teksten
• and in this pattern: jo bedre forstår jeg teksten

So the inversion forstår jeg is expected.

Because in the first half, jeg læser behaves more like a subordinate or relative-like clause attached to flere bøger.

So the structure is roughly:

• jo flere bøger
  • jeg læser

Here flere bøger is the object of læser, and the subject stays before the verb:

• jeg læser

That is why you get:

• jo flere bøger jeg læser

not:

• jo flere bøger læser jeg

So the two halves are not built in exactly the same way, even though they belong to the same overall pattern.

Teksten means the text.

Danish often uses the definite form when the speaker and listener both know which thing is being talked about. So teksten suggests a specific text already understood from the situation.

If you said en tekst, that would mean a text, not a specific one.

So:

• teksten = the text
• en tekst = a text

Because the sentence expresses a general relationship, not just one single event happening right now.

Danish often uses the present tense for things like:

• general truths
• habits
• repeated situations
• cause-and-effect patterns

So this works like English:

• The more I read, the better I understand

It is not limited to this exact moment.

Not normally, if you specifically mean more books.

If you want to focus on the number of books, use flere:

• Jo flere bøger jeg læser ...

If you want to focus on the activity of reading in general, use mere:

• Jo mere jeg læser ...

So:

• flere bøger = more books
• mere læsning / mere jeg læser = more reading

Jo mere jeg læser bøger is not the natural way to say it.

Yes.

You can also say:

Jo flere bøger jeg læser, desto bedre forstår jeg teksten.

This means the same thing. Many learners meet both patterns:

• jo ..., jo ...
• jo ..., desto ...

The jo ... jo ... version is very common and natural. Desto can sound a bit more formal or written.

Yes, the comma is standard here.

It separates the two parts of the comparative pattern:

• Jo flere bøger jeg læser, jo bedre forstår jeg teksten.

In normal written Danish, you should include that comma.