De uitleg is vrij duidelijk.

Because uitleg is a de-word in Dutch. Nouns in Dutch take either de or het, and this usually has to be learned with the noun.

So:

• de uitleg = the explanation

There is not always a logical reason you can see from the meaning alone, so it is best to memorize nouns together with their article:

• de uitleg
• het boek
• de tafel

Uitleg usually means explanation.

Depending on context, it can also feel like:

• an explanation
• instructions
• clarification
• an account of how something works

In De uitleg is vrij duidelijk, the most natural meaning is The explanation is quite clear.

This is a normal Dutch main clause, and the structure is very similar to English:

• De uitleg = subject
• is = verb
• vrij duidelijk = complement describing the subject

So literally:

• The explanation
  • is
    • quite clear

Dutch main clauses usually put the finite verb in second position, and that is exactly what happens here:

• De uitleg | is | vrij duidelijk

Yes, vrij can mean free, but here it does not mean that.

In this sentence, vrij means:

• quite
• rather
• fairly

So:

• vrij duidelijk = quite clear / fairly clear

This is a very common Dutch use of vrij.

Compare:

• Ik ben vrij. = I am free.
• Dat is vrij moeilijk. = That is quite difficult.

So the meaning depends on context.

Because duidelijk comes after the verb is and is used as a predicate adjective.

In Dutch:

• before a noun, adjectives usually take -e
• after zijn, worden, blijven, etc., they usually do not take -e

Compare:

• de duidelijke uitleg = the clear explanation
• de uitleg is duidelijk = the explanation is clear

So in your sentence, duidelijk is correct because it comes after is.

Here it is an adjective.

It describes de uitleg, so it tells you a quality of the explanation:

• The explanation is clear

The word vrij is modifying duidelijk, so vrij functions like quite/fairly does in English.

Structure:

• de uitleg = noun phrase
• is duidelijk = adjective describing the noun phrase
• vrij = modifies the adjective

Yes. All of these are possible, but they are slightly different in tone:

• vrij duidelijk = quite/fairly clear
• heel duidelijk = very clear
• erg duidelijk = very clear
• tamelijk duidelijk = rather/fairly clear

So:

• De uitleg is vrij duidelijk. sounds a bit more moderate.
• De uitleg is heel duidelijk. sounds stronger.

A rough English-friendly guide:

• uitleg ≈ OUT-lekh

  • ui is a Dutch vowel sound that does not exist exactly in English
  • the g is the Dutch throaty g/ch sound in many accents

• duidelijk ≈ DOY-de-luk or DOW-de-luk, very roughly

  • ui again is the tricky Dutch vowel
  • ij sounds somewhat like the vowel in English my, but not exactly

The hardest parts for English speakers are usually:

• ui
• ij
• the Dutch g

Yes, but in this sentence it is singular.

Singular:

• de uitleg = the explanation

Plural:

• de uitleggen is not normally used the way you might expect from regular noun patterns. In practice, Dutch often uses other wording depending on context, such as:
  • de verklaringen for the explanations
  • or a different phrasing entirely

For learners, the important thing here is just:

• De uitleg is ... = singular

Yes, absolutely.

• De uitleg is duidelijk. = The explanation is clear.
• De uitleg is vrij duidelijk. = The explanation is quite clear.

Adding vrij softens or shades the statement a little. It makes it sound less absolute than just duidelijk, depending on context.

Yes, it is completely natural and neutral.

It sounds like normal standard Dutch and could be used in many situations, for example when talking about:

• a teacher’s explanation
• written instructions
• a manual
• directions
• a presentation

It is a simple, everyday sentence that is very useful as a model for Dutch word order and adjective use.