Heiðurinn er mikill.

Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word like the.

• heiður = honor, glory (indefinite)
• heiðurinn = the honor, the glory (definite)

The ending -inn is the masculine nominative singular definite article here.

So Heiðurinn er mikill uses the definite form: the honor is great.

Heiður is a masculine noun. That matters because adjectives in Icelandic must agree with the noun they describe in:

• gender
• number
• case

Since heiðurinn is masculine singular nominative, the adjective also appears in the matching form:

• mikill = masculine singular nominative

If the noun were feminine or neuter, the adjective form would be different.

Because mikill has to match heiðurinn.

In this sentence:

• heiðurinn = masculine
• singular
• nominative

So the adjective must also be:

• masculine
• singular
• nominative

That gives mikill.

This is a very important Icelandic pattern: after vera (to be), the adjective still agrees with the subject.

Yes.

In a sentence like this:

• Heiðurinn is the subject
• er is the verb
• mikill is a predicate adjective

In Icelandic, predicate adjectives after vera usually stand in the nominative and agree with the subject.

So both words are nominative singular masculine here:

• heiðurinn
• mikill

Not exactly. Mikill often means something like:

• great
• large
• considerable
• much (depending on context)

With something abstract like heiður (honor), English would usually say great rather than big.

So Heiðurinn er mikill is more like:

• The honor is great
• It is a great honor

rather than The honor is big.

Yes, but it changes the feel of the sentence.

• Heiðurinn er mikill = the honor is great / a specific honor is being referred to
• Heiður er mikill = honor is great / honor is important / a more general statement

So the version with -inn is more specific and usually sounds more natural if you are talking about a particular honor.

Er is the third person singular present of vera (to be).

So:

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

In Heiðurinn er mikill, er simply means is.

No, this is the normal basic Icelandic word order:

• Heiðurinn = subject
• er = verb
• mikill = complement/adjective

So it follows the familiar pattern:

Subject + verb + adjective

Icelandic can sometimes move words around for emphasis, poetry, or style, but this sentence is straightforward and neutral.

The letter ð in Icelandic is usually like the th in English this.

So Heiður- has a sound roughly like:

• HEY-thur or HAY-thur

Very roughly, Heiðurinn can be approximated for English speakers as:

• HAY-thur-rin

But that is only approximate. The real Icelandic pronunciation is subtler, especially the vowels and the rolled/trilled r.

Yes, it is somewhat irregular and very common, so it is worth learning early.

Its forms do not behave as simply as some more regular adjectives. For example, its endings change noticeably across gender and case.

In this sentence, you only need the form:

• mikill = masculine nominative singular

But it is useful to remember that this adjective is one of those high-frequency words whose forms should be learned carefully over time.

Because Icelandic usually expresses the with a suffix attached to the noun.

So instead of:

• separate word + noun

you often get:

• noun + definite ending

That is why heiðurinn already includes the meaning the honor.

Icelandic can use a separate demonstrative-like word in some contexts, but the normal definite article is the ending attached to the noun.