Skýringin hjálpar mér að skilja þetta.

The ending -in is the definite article attached to the noun, so skýringin means the explanation.

In Icelandic, the definite article is usually added to the end of the noun rather than written as a separate word. So:

• skýring = an explanation / explanation
• skýringin = the explanation

It is in the nominative singular. It is the subject of the sentence, the thing doing the helping.

The basic structure is:

Skýringin + hjálpar + mér + að skilja þetta
The explanation + helps + me + to understand this

Since skýringin is the subject, nominative is what you expect.

Because the verb hjálpa normally takes the dative case for the person being helped.

So:

• ég = I
• mig = me, accusative
• mér = me, dative

With hjálpa, Icelandic uses dative:

• Hún hjálpar mér. = She helps me.
• Þetta hjálpar honum. = This helps him.

So in your sentence, mér is there because hjálpa einhverjum means to help someone, with someone in the dative.

Hjálpar is the 3rd person singular present tense of hjálpa.

So it matches skýringin, which is singular:

• ég hjálpa = I help
• þú hjálpar = you help
• hann / hún / það hjálpar = he / she / it helps

Since skýringin is grammatically singular, you use hjálpar.

Here að marks the infinitive, like English to in to understand.

So:

• skilja = understand
• að skilja = to understand

In this sentence, hjálpa mér að skilja þetta means helps me to understand this.

This is a very common pattern in Icelandic:
verb + object + að + infinitive

For example:

• Hún reynir að lesa. = She tries to read.
• Þetta hjálpar mér að muna. = This helps me remember.

Yes. It functions like an infinitive phrase.

The main clause is:

Skýringin hjálpar mér

Then að skilja þetta tells you what the explanation helps you do.

So the sentence is basically:

The explanation helps me + to understand this

That whole phrase is closely tied to hjálpar.

Þetta is the neuter singular form of this.

It can mean:

• this
• this thing
• this matter / this point
• sometimes this situation, depending on context

It is often used when referring to something previously mentioned, something abstract, or something whose noun is not being repeated.

For example:

• Ég skil þetta. = I understand this.
• Þetta er erfitt. = This is difficult.

It is in the accusative here, because it is the direct object of skilja.

You are understanding this, so þetta is the thing being understood.

For neuter singular demonstratives, the form þetta can look the same in nominative and accusative, so you identify the case from the role it plays in the sentence.

Yes, that is a perfectly natural English way to express the same idea.

Icelandic present tense often covers both:

• simple present: helps
• present progressive: is helping

So Skýringin hjálpar mér að skilja þetta could be translated as either:

• The explanation helps me understand this
• The explanation is helping me understand this

Which English version sounds best depends on context.

The given word order is the most straightforward and neutral one:

Skýringin hjálpar mér að skilja þetta.

But Icelandic word order is somewhat flexible because case endings show grammatical roles. Still, not every rearrangement sounds equally natural.

For example, you might also see emphasis patterns like:

• Mér hjálpar skýringin að skilja þetta.
  This gives more focus to mér.

But for a learner, the original order is the safest and most natural.

A rough English-style approximation would be:

SKEE-ring-in hyaul-par myair ath skilh-ya THET-ta

A few useful pronunciation notes:

• ský sounds roughly like skee
• ring in skýringin has a clear Icelandic r
• hj in hjálpar is not like normal English h + j; it has a soft, voiceless y-like quality
• á is a diphthong, roughly like ow or au in some approximations
• að is often pronounced with a soft th sound, like in this, though pronunciation can vary in connected speech
• þ in þetta is the th of thin, not the th of this

Here are the dictionary forms:

• skýringin → skýring = explanation
• hjálpar → hjálpa = to help
• mér → pronoun ég = I
• að = infinitive marker to
• skilja = to understand
• þetta → demonstrative þessi / þetta = this

This is useful because Icelandic words often appear in changed forms depending on case, number, gender, tense, and function in the sentence.