Kötturinn skríður undir sófann þegar gestirnir koma.

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

• köttur = cat
• kötturinn = the cat
• gestir = guests
• gestirnir = the guests
• sófa-/sófann = the sofa in the form required here

So in this sentence, kötturinn, gestirnir, and sófann already include the idea of the.

Kötturinn is the nominative singular definite form of köttur.

• köttur = a cat / cat
• kötturinn = the cat

It is nominative because it is the subject of the sentence: the cat is the one doing the action.

Because undir can take different cases depending on meaning.

Here, the cat is moving to a place under the sofa, so Icelandic uses the accusative:

• undir sófann = under the sofa, with movement toward that position

If the cat were already there and just staying there, Icelandic would normally use the dative:

• undir sófanum = under the sofa, in a static location

This is a very common Icelandic pattern with prepositions.

You would normally use a verb of being or staying, and undir would take the dative:

• Kötturinn er undir sófanum. = The cat is under the sofa.

So the contrast is:

• skríður undir sófann = crawls/goes under the sofa
• er undir sófanum = is under the sofa

Skríður is the present tense of skríða.

Its basic meaning is crawls, but depending on context it can also sound like:

• creeps
• crawls
• slinks
• goes slowly under

With a cat, English may translate it naturally in different ways depending on the situation. Icelandic is being a bit more vivid than just goes.

Because the subject is plural: gestirnir = the guests.

The verb koma changes according to person and number:

• gesturinn kemur = the guest comes
• gestirnir koma = the guests come

So koma is the correct present-tense form for a third-person plural subject.

Here þegar means when and introduces a time clause:

• þegar gestirnir koma = when the guests come

A common source of confusion is that þegar can also mean already in other contexts. But in this sentence it is clearly the conjunction when, because it is followed by a whole clause.

Because this is a subordinate clause introduced by þegar.

In that clause, the usual order is:

• conjunction + subject + verb

So:

• þegar
  • gestirnir
    • koma

That is why you get þegar gestirnir koma = when the guests come.

A useful comparison:

• Kötturinn skríður undir sófann þegar gestirnir koma.
• Þegar gestirnir koma, skríður kötturinn undir sófann.

Both are natural, but the second one starts with the time clause.

Most naturally, it sounds habitual or general:

• The cat crawls under the sofa when the guests come.

In other words, this is what the cat typically does whenever guests arrive.

Icelandic present tense, like English present tense, can often describe repeated or habitual behavior, not only something happening at this exact moment.

Because several changes are happening at once:

1. gestur is singular: guest
2. gestir is plural: guests
3. gestirnir is definite plural: the guests

So the ending shows both:

• plural
• the

This kind of noun change is very normal in Icelandic, where number, case, and definiteness are all built into the form.

A few useful pronunciation notes:

• Icelandic stress is usually on the first syllable
• þ is like th in thin
• ð is like th in this
• r is usually tapped or rolled lightly

Word notes:

• Kötturinn: the ö is somewhat like German ö or French eu
• skríður: í is a long ee sound
• þegar: starts with th as in thin
• gestirnir: the r should be pronounced, not dropped
• sófann: the ó is like a long o

Even if your pronunciation is not perfect yet, getting þ and ð roughly right will already help a lot.