Hún sýður kartöflur í litlum potti meðan ég set diskana á borðið.

Sjóða is the dictionary form, meaning to boil. In the sentence, the verb has to be conjugated, and the 3rd person singular present form is sýður.

So:

• sjóða = to boil
• ég sýð = I boil / am boiling
• hún sýður = she boils / is boiling

This is an irregular verb, so the stem changes from sjóð- to sýð- in the present.

It can mean either, depending on context. Icelandic often uses the simple present where English might prefer the present progressive.

So Hún sýður kartöflur can mean:

• She boils potatoes
• She is boiling potatoes

In a sentence like this, the ongoing meaning is boiling is usually what an English speaker would understand.

Kartöflur is the plural form of kartafla, meaning potato. Here it is the direct object of the verb sýður, so it appears in the accusative plural form.

Useful forms:

• kartafla = a potato
• kartöflur = potatoes

So sýður kartöflur means boils potatoes or is boiling potatoes.

Icelandic often does not use a separate word like English the. Instead, definiteness is usually shown with an ending attached to the noun.

Here, kartöflur is indefinite and means simply potatoes, not the potatoes.

If you wanted the potatoes, you would normally say kartöflurnar.

Because the preposition í means in, and when it refers to location, it takes the dative case. Since the potatoes are located in a small pot, both the adjective and the noun appear in dative singular.

So:

• pottur = pot
• potti = in a pot / in the pot, depending on context
• litlum = small, dative singular masculine

The adjective litlum agrees with potti in case, number, and gender.

The basic form is lítill, meaning small, but adjectives change form to match the noun they describe.

Since potti is:

• masculine
• singular
• dative

the adjective must also be masculine singular dative, which gives litlum.

So:

• lítill pottur = a small pot
• í litlum potti = in a small pot

Meðan means while. It introduces a clause that describes something happening at the same time as the action in the main clause.

So:

• Hún sýður kartöflur ... meðan ég set diskana á borðið
• She is boiling potatoes ... while I put the plates on the table

It connects the two simultaneous actions.

Setja is the infinitive, meaning to put or to set. After the subject ég, you need the conjugated present-tense form, which is set.

So:

• setja = to put
• ég set = I put / I am putting

That is why the sentence has ég set diskana á borðið.

Diskana is the definite accusative plural form of diskur, meaning plate. The ending shows that the noun means the plates, not just plates.

Compare:

• diska = plates
• diskana = the plates

It is accusative plural because diskana is the direct object of set.

This is a very common Icelandic pattern. The preposition á can take either accusative or dative, depending on meaning:

• accusative for movement toward a place
• dative for location in a place

Here, the plates are being moved onto the table, so Icelandic uses the accusative: á borðið.

Compare:

• Ég set diskana á borðið = I put the plates onto the table
• Diskarnir eru á borðinu = The plates are on the table

Yes. Borð means table, and borðið means the table. Icelandic usually adds the definite article to the end of the noun instead of putting a separate word before it.

So:

• borð = table
• borðið = the table

In this sentence, it is also in the accusative, but for neuter nouns like borð, the nominative and accusative singular often look the same.

Yes, a little. In the main clause, Icelandic often follows the verb-second pattern, but after a subordinating word like meðan, the clause normally begins with the subject followed by the verb.

So here:

• meðan ég set diskana á borðið

This is a normal subordinate clause order: meðan + subject + verb.

Yes, Icelandic can use vera að + infinitive to emphasize an ongoing action, for example Hún er að sjóða kartöflur. But in many ordinary sentences, Icelandic simply uses the present tense, as in Hún sýður kartöflur.

So the sentence as given is completely natural, even though English often prefers is boiling and am putting.