Forholdet er vigtigt.

It is an et word: et forhold.

That matters because:

• the definite singular becomes forholdet = the relationship / the situation / the matter, depending on context
• adjectives that go with a singular neuter noun often take -t, which is why you get vigtigt

So this sentence gives you two clues that forhold is neuter:

• forholdet
• vigtigt

The -et is the definite article attached to the noun.

So:

• et forhold = a relationship / a situation
• forholdet = the relationship / the situation

Unlike English, Danish often puts the at the end of the noun instead of using a separate word.

Because Danish usually expresses the by adding an ending to the noun.

Here:

• English: the relationship
• Danish: forholdet

This is very common in Danish:

• et hus = a house
• huset = the house
• en bil = a car
• bilen = the car

So forholdet already includes the idea of the.

Because vigtig changes form to agree with the noun.

The adjective vigtig means important, but its form depends on grammar:

• vigtig → common gender singular
• vigtigt → neuter singular
• vigtige → plural or certain definite uses

Since forholdet is a singular et noun, Danish uses:

• Forholdet er vigtigt.

Compare:

• Bilen er vigtig. = The car is important.
  (bil is an en word)
• Huset er vigtigt. = The house is important.
  (hus is an et word)

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

So in this sentence:

• Forholdet er vigtigt.
• literally: The relationship is important.

Some other forms of at være:

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

The basic order here is:

subject + verb + adjective/complement

So:

• Forholdet = subject
• er = verb
• vigtigt = complement

This is very similar to English:

• The relationship is important.

In a simple statement like this, Danish word order feels very familiar to English speakers.

No. Forhold is a flexible word in Danish, and its exact meaning depends on context.

It can mean things like:

• relationship
• situation
• condition(s)
• circumstance(s)
• matter / issue

So Forholdet er vigtigt could mean different things depending on the situation, even though the grammar stays the same.

That is very normal in Danish vocabulary: one word may cover several related meanings.

If you want a relationship instead of the relationship, you use the indefinite form:

• Et forhold er vigtigt.

Compare:

• et forhold = a relationship
• forholdet = the relationship

So:

• Et forhold er vigtigt. = A relationship is important.
• Forholdet er vigtigt. = The relationship is important.

In the plural, both the noun and the adjective change.

Examples:

• Forhold er vigtige. = Relationships / conditions are important.
• Forholdene er vigtige. = The relationships / the conditions are important.

Notice:

• singular definite: forholdet er vigtigt
• plural indefinite: forhold er vigtige
• plural definite: forholdene er vigtige

Also notice that the adjective becomes vigtige in the plural.

A rough learner-friendly guide is:

• forholdet → for-HOL-det
• er → a short weak air / er sound
• vigtigt → roughly VEK-tit

Two useful tips:

• the stress in forholdet is on HOL
• vigtigt is not pronounced exactly the way an English speaker might expect from the spelling; in natural speech, some sounds are reduced

Danish pronunciation varies a bit by speaker and region, so it is best to treat this as an approximation and listen to native audio if possible.