Isoleringen er vigtig.

Because Danish usually adds the definite article to the end of the noun instead of putting a separate word in front.

• isolering = insulation
• isoleringen = the insulation

The ending -en is the singular definite ending for many common-gender nouns.

So:

• en isolering = an insulation / insulation
• isoleringen = the insulation

That depends on the noun’s grammatical gender.

In Danish, singular nouns are mainly:

• common gender: take en
• neuter gender: take et

Isolering is a common-gender noun, so its forms are:

• en isolering
• isoleringen

Unfortunately, gender usually has to be learned with the noun. A good habit is to memorize nouns with their article:

• en isolering
• et hus
• en bil

Er means is / are / am in the present tense, depending on context. It is the present tense of at være = to be.

So here:

• Isoleringen er vigtig = The insulation is important

Some other forms of at være:

• jeg er = I am
• du er = you are
• han er = he is
• vi er = we are

Unlike English, Danish uses the same present-tense form er for all persons.

Because the adjective agrees with the noun’s gender and number.

Here, the subject is isoleringen, which is:

• singular
• common gender

For a singular common-gender noun, the adjective usually stays in its basic form:

• vigtig

Compare:

• en vigtig ting = an important thing
• isoleringen er vigtig = the insulation is important

But with a neuter singular noun, you usually add -t:

• et vigtigt problem = an important problem
• problemet er vigtigt = the problem is important

And with plural, you usually use -e:

• vigtige ting = important things
• tingene er vigtige = the things are important

Because this adjective is being used predicatively — that means it comes after er and describes the subject.

In Danish, adjectives behave differently depending on where they are used:

1. Attributive adjective

When the adjective comes before the noun:

• den vigtige isolering = the important insulation

Here you get vigtige.

2. Predicative adjective

When the adjective comes after er:

• isoleringen er vigtig = the insulation is important

Here the adjective agrees mainly with gender and number, not with definiteness in the same way. Since isoleringen is singular common gender, vigtig is correct.

Yes, but the meaning changes.

• Isolering er vigtig = Insulation is important
  
  • a general statement
• Isoleringen er vigtig = The insulation is important
  
  • a specific insulation, or the insulation in a specific situation

So the sentence with -en sounds more specific.

The dictionary form is isolering.

When you look up Danish nouns, you usually want the indefinite singular form, often together with the article:

• en isolering

So if you see isoleringen, you can strip off the definite ending -en and look for isolering.

No, this is a very standard Danish main clause:

• Isoleringen = subject
• er = verb
• vigtig = adjective/complement

So it follows the basic pattern:

Subject + verb + complement

That makes it very similar to English:

• The insulation is important

A rough learner-friendly approximation is:

ee-so-leh-RING-en air VIG-ti

A few useful notes:

• isoleringen has its main stress on -RING-
• er is often pronounced very lightly in normal speech
• vigtig does not sound exactly like English vig-tig; the final part is softer and shorter than an English speaker might expect

If you want to sound more natural, it is best to learn this one by listening and repeating, because Danish pronunciation is often less phonetic than the spelling suggests.

Its main meaning is important.

Depending on context, it can also feel like:

• significant
• important to pay attention to
• of importance

But important is the safest and most direct translation here.

So in this sentence, vigtig is exactly the normal word you would expect.