Sjálfsafgreiðslan er auðveld.

The -n is the definite article attached to the noun, so sjálfsafgreiðslan means the self-service.

In Icelandic, the word for the is usually not a separate word like in English. Instead, it is added to the end of the noun.

• sjálfsafgreiðsla = self-service
• sjálfsafgreiðslan = the self-service

Because sjálfsafgreiðsla is a feminine noun ending in -a, the definite form becomes -an in the nominative singular:

• afgreiðsla → afgreiðslan
• sjálfsafgreiðsla → sjálfsafgreiðslan

Yes. Icelandic very often makes compound words, much more freely than English.

sjálfsafgreiðsla is built from:

• sjálfs- = self-
• afgreiðsla = service, checkout, transaction/service handling

So the whole word means something like self-service or, depending on context, self-checkout.

This is very normal in Icelandic. English often uses two words or a hyphen, but Icelandic commonly writes it as one word.

Because the adjective has to agree with the noun in gender and number.

sjálfsafgreiðslan is:

• singular
• feminine
• nominative (as the subject)

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

• masculine: auðveldur
• feminine: auðveld
• neuter: auðvelt

That is why the sentence uses auðveld.

Because here the adjective is being used predicatively, not directly attached to the noun.

Compare:

• Sjálfsafgreiðslan er auðveld. = The self-service is easy.
  
  • auðveld comes after er
• auðveld sjálfsafgreiðsla = easy self-service
  
  • the adjective comes directly before the noun

So in this sentence, auðveld is describing the subject through the verb er (is), which is why it comes after the verb.

er is the present tense singular form of the verb vera (to be).

So here:

• er = is

A few common forms of vera are:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is
• við erum = we are
• þið eruð = you are
• þeir/þær/þau eru = they are

In this sentence, the subject is singular, so er is the correct form.

Because Icelandic usually expresses the by adding it to the end of the noun instead of putting a separate article in front.

So instead of something like:

• the self-service

Icelandic normally says:

• sjálfsafgreiðslan

This is one of the biggest structural differences from English.

Icelandic can also use a separate article-like word in some formal or special contexts, but for normal everyday noun phrases, the suffixed article is standard.

Yes, it is feminine.

The base noun is sjálfsafgreiðsla, and nouns ending in -a are very often feminine in Icelandic, though not always with 100% certainty in every case. Here, it definitely is feminine.

You can also tell from the adjective:

• auðveld is feminine singular
• if the noun were masculine, it would be auðveldur
• if it were neuter, it would be auðvelt

So the sentence itself confirms the noun’s gender.

It is in the nominative case because it is the subject of the sentence.

In Sjálfsafgreiðslan er auðveld:

• sjálfsafgreiðslan = the subject
• er = is
• auðveld = a predicate adjective describing the subject

Subjects are normally in the nominative in Icelandic, just as in many other languages.

Yes. Even though auðveld comes after the verb, it still agrees with the subject and is understood as nominative feminine singular here.

With vera (to be), predicate adjectives normally match the subject in:

• gender
• number
• case

So because sjálfsafgreiðslan is nominative feminine singular, auðveld is too.

A rough English-friendly guide would be something like:

SYAHLFS-a-greyths-lan er OY-thveld

A few useful pronunciation notes:

• sj is often pronounced a bit like sy
• á is like ow in cow, but longer
• ei is usually like ay in day
• ð is like the th in this
• au is like oy in boy

The pronunciation can vary a little by speaker, but those approximations will get you fairly close.

Yes, but Sjálfsafgreiðslan er auðveld is the most basic and neutral order.

Icelandic is a verb-second language, which means the finite verb often comes in the second position in main clauses. If you move another element to the front for emphasis, the verb still usually stays second.

For example, in a larger context you might see different word orders, but the normal plain statement is:

• Sjálfsafgreiðslan er auðveld.

That is the best version to learn first.

Yes, but the meaning becomes more general.

• Sjálfsafgreiðslan er auðveld. = The self-service is easy.
• Sjálfsafgreiðsla er auðveld. = Self-service is easy.

So the version with -n points to a specific self-service system or instance, while the version without it sounds more general or abstract.