Hugurinn er rólegur.

Hugur is the basic dictionary form and means mind.
Hugurinn is the definite form and means the mind.

Icelandic usually makes nouns definite by adding the article to the end of the noun, instead of using a separate word like English the.

• hugur = mind
• hugurinn = the mind

So in this sentence, hugurinn is the natural form because the noun is definite.

Er means is.

It is the 3rd person singular present tense of the verb að vera = to be.

A few present-tense forms are:

• ég er = I am
• þú ert = you are
• hann / hún / það er = he / she / it is

So Hugurinn er rólegur has the same basic structure as English: The mind is calm.

Because Icelandic adjectives must agree with the noun they describe in gender, number, and case.

Here, hugurinn is:

• masculine
• singular
• nominative

So the adjective also appears in the masculine singular nominative form:

• rólegur = calm

Compare:

• masculine: rólegur
• feminine: róleg
• neuter: rólegt

So the ending -ur is there because the subject is a masculine singular noun.

Because this sentence is using rólegur as a predicate adjective, not as an adjective directly attached to the noun.

Structure here:

• Hugurinn = the subject
• er = is
• rólegur = predicate adjective

So the pattern is:

subject + to be + adjective

That is very similar to English:

• The mind is calm

If you wanted the adjective directly before the noun, you would be making a noun phrase instead:

• rólegur hugur = a calm mind

So:

• Hugurinn er rólegur = the mind is calm
• rólegur hugur = a calm mind

This is a very common thing for learners to notice.

In Hugurinn er rólegur, the adjective is predicative: it comes after er and describes the subject. In that position, Icelandic uses the strong adjective form:

• rólegur

But in a definite noun phrase like rólegi hugurinn = the calm mind, the adjective stands directly with a definite noun. In that position, Icelandic normally uses the weak adjective form:

• rólegi hugurinn = the calm mind

So:

• hugurinn er rólegur = the mind is calm
• rólegi hugurinn = the calm mind

That difference is grammatical, not a difference in meaning like more calm or anything like that.

Not by using a different verb.

Icelandic uses vera = to be in both cases. Unlike languages such as Spanish, there is no built-in ser/estar type distinction here.

So Hugurinn er rólegur could describe:

• a calm state right now
• a more general condition
• a calm mindset in context

You understand which one is meant from the situation, not from a special form of the verb.

Yes. Hugur is a broad word, and its exact sense depends on context.

It can refer to things like:

• mind
• thought
• state of mind
• spirit
• inclination
• sometimes even courage or feeling

In Hugurinn er rólegur, the sense is most naturally something like the mind or the state of mind, because rólegur suggests calmness or inner quiet.

To make it a question, Icelandic usually puts the verb first:

• Er hugurinn rólegur? = Is the mind calm?

To make it negative, add ekki:

• Hugurinn er ekki rólegur. = The mind is not calm.

So the key patterns are:

• statement: Hugurinn er rólegur.
• question: Er hugurinn rólegur?
• negative: Hugurinn er ekki rólegur.

A few useful pronunciation points:

• Icelandic stress is usually on the first syllable of each word.
• ó in rólegur is a long vowel, roughly like a clear o sound.
• r is typically tapped or trilled, not the usual English r.
• g between vowels is often softer than a hard English g.

A rough learner-friendly guide would be something like:

HU-gu-rinn er RO-le-gur

But that is only approximate. The real Icelandic sounds are a bit different from English, especially the vowels and the r.