Traust er mikilvægt þegar fólk vinnur saman.

Traust means trust here.

It is a neuter noun in Icelandic. In different contexts, it can also suggest confidence or reliability, but in this sentence the natural meaning is trust in the general sense.

So:

• Traust = trust
• Traust er mikilvægt = Trust is important

Because mikilvægur is an adjective that changes form to match the noun it describes.

The forms are:

• mikilvægur = masculine
• mikilvæg = feminine
• mikilvægt = neuter

Since traust is neuter singular, the adjective must also be neuter singular, so you get:

• Traust er mikilvægt

This is very common in Icelandic: adjectives agree with the noun in gender, number, and often case.

Because Icelandic often leaves out the definite article when speaking about something in general.

This sentence is making a general statement:

• Traust er mikilvægt = Trust is important
• fólk vinnur saman = people work together / people are working together

English also often does this with abstract nouns:

• Trust is important
• not necessarily The trust is important

So the lack of the is normal here.

Because fólk is a collective noun in Icelandic. It refers to people as a group, but grammatically it is singular.

That is why the verb is also singular:

• fólk vinnur = people work

Even though this sounds odd from an English point of view, it is completely normal in Icelandic.

Also note that fólk is neuter singular.

Because the subject is fólk, and fólk is grammatically singular.

So Icelandic uses the singular verb form:

• fólk vinnur = people work / people are working

The verb vinnur is the 3rd person singular present of vinna.

So:

• að vinna = to work
• ég vinn = I work
• þú vinnur = you work
• hann/hún/það vinnur = he/she/it works

Here, fólk behaves like það in grammar, so vinnur is the correct form.

Here, þegar means when.

So:

• þegar fólk vinnur saman = when people work together

In other contexts, þegar can sometimes mean once or be used in slightly different time-related ways, but when is the right meaning here.

It introduces a subordinate clause.

Both are in the nominative case.

Why?

• Traust is the subject of the main clause: Traust er mikilvægt
• fólk is the subject of the subordinate clause: þegar fólk vinnur saman

So both appear in their basic subject form.

Also, the adjective mikilvægt is in the form that matches traust: neuter singular nominative.

Saman means together.

So:

• vinna saman = work together

It is an adverb, and in this sentence it comes after the verb:

• fólk vinnur saman

That is a very natural placement in Icelandic.

You will often see saman used this way in set expressions like:

• vera saman = be together
• gera eitthvað saman = do something together
• vinna saman = work together

Yes. You can say:

• Þegar fólk vinnur saman er traust mikilvægt.

That is completely natural.

When the subordinate clause comes first, the main clause follows it. Icelandic still keeps its normal sentence structure rules, so this version is good and idiomatic.

Both orders work:

• Traust er mikilvægt þegar fólk vinnur saman.
• Þegar fólk vinnur saman er traust mikilvægt.

The first version starts with the main point: Trust is important.
The second version starts with the situation: When people work together.

It can mean more than just to work.

Að vinna can mean:

• to work
• to do work
• sometimes to win, depending on context

For example:

• Ég vinn á skrifstofu = I work in an office
• Liðið vann leikinn = The team won the game

In your sentence, fólk vinnur saman, it clearly means people work together.

A rough English-style guide would be:

Traust er mik-il-vaiht yeh-thar folk vin-nur sa-man

A few useful pronunciation notes:

• au in traust is not like English ow exactly, but that rough guide helps.
• æ in mikilvægt is pronounced somewhat like eye.
• þ in þegar is like th in thin, not like th in this.
• ö does not appear here, but ó and ú would be different vowels; Icelandic vowel spelling matters a lot.
• The g in mikilvægt is not pronounced like a strong English g.

If you want to sound more natural, it is best to listen to native audio, because Icelandic pronunciation does not map neatly onto English spelling.

The sentence has two parts:

1. Traust er mikilvægt

   • Traust = subject
   • er = is
   • mikilvægt = predicate adjective

2. þegar fólk vinnur saman

   • þegar = when
   • fólk = subject
   • vinnur = works
   • saman = together

So the full structure is:

• [Main clause] + [subordinate clause]
• Trust is important + when people work together

This is a very common and useful Icelandic sentence pattern.