Jeg forstår holdningen bedre, når hun forklarer den roligt.

Holdningen is the definite form, meaning the attitude / the opinion / the stance rather than an attitude.

In Danish, the definite article is usually attached to the end of the noun:

• en holdning = an attitude, an opinion
• holdningen = the attitude, the opinion

So this sentence is talking about a specific attitude that is already known from the context.

Den refers back to holdningen.

So instead of repeating the noun, Danish uses an object pronoun:

• holdningen = the attitude/opinion
• den = it

This is very similar to English:

• I understand the attitude better when she explains it calmly.

Because holdning is a common-gender noun, the pronoun is den, not det.

Danish nouns belong to one of two grammatical genders:

• common gender → usually takes en and later den
• neuter gender → usually takes et and later det

Holdning is a common-gender noun:

• en holdning
• holdningen
• den

So den is the correct pronoun.

Because roligt is being used as an adverb.

• rolig = calm (adjective)
• roligt = calmly (adverb)

Here it describes how she explains it, so Danish uses the adverb form:

• hun er rolig = she is calm
• hun forklarer den roligt = she explains it calmly

A very common pattern in Danish is that an adjective gets -t when used adverbially.

Bedre is the comparative form meaning better.

Just like English has an irregular form:

• good → better

Danish has:

• god = good
• godt = well / good
• bedre = better

So:

• Jeg forstår det bedre = I understand it better

Using mere godt would sound wrong here.

Here når means when or whenever.

It introduces a subordinate clause:

• når hun forklarer den roligt = when she explains it calmly

In this sentence, it has a general, repeated sense: every time or whenever she explains it calmly, I understand it better.

This is a very common question.

• når = when / whenever
• hvis = if

So:

• Jeg forstår holdningen bedre, når hun forklarer den roligt.
  = I understand the attitude better when/whenever she explains it calmly.

• Jeg forstår holdningen bedre, hvis hun forklarer den roligt.
  = I understand the attitude better if she explains it calmly.

The first sounds like a regular pattern. The second sounds more conditional.

Because Danish normally uses a comma before a subordinate clause.

Here the main clause is:

• Jeg forstår holdningen bedre

And the subordinate clause is:

• når hun forklarer den roligt

So the comma helps separate them. This is very standard in written Danish.

Because Danish main clauses and subordinate clauses follow different word-order rules.

In a main clause, Danish normally has verb-second word order:

• Hun forklarer den roligt.

But after a subordinating conjunction like når, Danish uses subordinate clause order:

• når hun forklarer den roligt

So after når, the subject hun comes before the finite verb forklarer.

Because the neutral word order here is:

verb + object + adverb

So:

• forklarer den roligt = explains it calmly

This is the most natural order in this sentence.
Putting roligt before den would sound wrong here.

Compare:

• Hun forklarer den roligt. = natural
• Hun forklarer roligt den. = not natural

Yes, forklarer is present tense.

The sentence uses the present because it describes a general situation or repeated truth:

• I understand the attitude better when she explains it calmly.

This is similar to English, which also often uses the present tense for general truths and habits.

Yes, that is a very helpful way to understand it.

The sentence has:

1. a main clause

   • Jeg forstår holdningen bedre
   • I understand the attitude better

2. a subordinate clause

   • når hun forklarer den roligt
   • when she explains it calmly

So the overall structure is:

main clause + subordinate clause

That is a very common Danish sentence pattern.