Misskilningurinn hvarf þegar hún útskýrði rólega hvað hún meinti.

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

• misskilningur = misunderstanding
• misskilningurinn = the misunderstanding

Here, -urinn is the nominative singular definite ending for this masculine noun.

It is in the nominative singular because it is the subject of the sentence — the thing that disappeared.

The verb is hvarf (disappeared/vanished), and the subject performing that action is Misskilningurinn.

Hvarf is the past tense of the verb hverfa (to disappear, vanish), and this is a strong verb, so its past tense is irregular.

• infinitive: hverfa
• past singular: hvarf
• past plural: hurfu

So Misskilningurinn hvarf means The misunderstanding disappeared.

Here þegar means when and introduces a subordinate clause:

• þegar hún útskýrði... = when she explained...

In other contexts, þegar can also mean already, so learners often need to use context to tell which meaning is intended.

Hún is the nominative singular pronoun meaning she. It is the subject of the subordinate clause:

• hún útskýrði = she explained

Since she is doing the explaining, the nominative form is required.

Útskýrði is the past tense, 3rd person singular of útskýra (to explain).

So:

• að útskýra = to explain
• hún útskýrði = she explained

This is a weak verb, so its past-tense formation is more regular than hverfa → hvarf.

Because rólega is the adverb form, meaning calmly.

• rólegur / róleg / rólegt = calm (adjective)
• rólega = calmly (adverb)

Since it describes how she explained, Icelandic uses the adverb:

• hún útskýrði rólega = she explained calmly

A very common pattern is that the neuter singular form of an adjective is used adverbially.

Here hvað means what and introduces an embedded clause:

• hvað hún meinti = what she meant

It is not a question word here in the sense of asking a direct question. Instead, it connects the verb útskýrði with the content of what she explained.

Meinti is the past tense of meina (to mean).

• að meina = to mean
• hún meinti = she meant

In hvað hún meinti, the past tense fits the past-time context of the whole sentence:

• she explained ... what she meant

English and Icelandic both often use past tense here because the explaining happened in the past.

It is an embedded clause with the meaning what she meant.

Word by word:

• hvað = what
• hún = she
• meinti = meant

So the sentence contains a clause inside a clause:

• main clause: Misskilningurinn hvarf
• time clause: þegar hún útskýrði rólega hvað hún meinti
• inside that: hvað hún meinti

Because rólega modifies the verb útskýrði and tells us how she explained. The phrase hvað hún meinti is the content of what she explained.

So the structure is:

• hún útskýrði = she explained
• rólega = calmly
• hvað hún meinti = what she meant

Together: she explained calmly what she meant

That word order is very natural in Icelandic.

Yes, but in a fairly straightforward way.

In the main clause:

• Misskilningurinn hvarf
  Subject + verb

In the subordinate clause introduced by þegar:

• þegar hún útskýrði rólega hvað hún meinti

This also looks quite similar to English, but it is useful to notice that Icelandic main clauses usually follow the verb-second (V2) pattern. In this sentence, nothing unusual happens, so the order feels simple and natural.

A rough English-friendly approximation would be:

MIS-skihl-ning-ur-inn kvarv THYE-gar hoon OOT-sky-rthih RO-leh-ga kvath hoon MAYN-tih

A few useful points:

• hv is usually pronounced like kv
• ð is like the th in this
• á / ý / í are long vowel sounds
• stress usually falls on the first syllable of each word

This is only an approximation, but it can help you get started.