Athugasemdin í bókinni hjálpar mér að skilja textann betur.

Athugasemdin is the noun athugasemd with the definite article attached.

• athugasemd = comment, remark, or note
• -in = the

So:

• athugasemd = a comment / a note
• athugasemdin = the comment / the note

Icelandic usually adds the to the end of the noun instead of using a separate word like English does.

In this sentence, athugasemdin is in the nominative singular, because it is the subject of the sentence.

Because í often takes the dative when it means in or inside something in a static location.

Here, the comment is located in the book, not moving into it, so Icelandic uses the dative:

• bók = book
• bókin = the book (nominative)
• bókinni = the book (dative)

So:

• í bókinni = in the book

This is a very common pattern:

• í húsinu = in the house
• í skólanum = in the school

If there were movement into something, Icelandic might use a different case.

Because the verb hjálpa normally takes a dative object in Icelandic.

The forms of I / me are:

• ég = nominative
• mig = accusative
• mér = dative

Since hjálpa einhverjum means to help someone, and einhverjum is dative, the sentence needs:

• hjálpar mér = helps me

This is something English speakers often need to get used to: Icelandic verbs often require specific cases for their objects.

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

The subject is athugasemdin, which is singular, so the verb is singular too:

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

So here:

• Athugasemdin ... hjálpar mér = The comment ... helps me

Here að skilja is an infinitive phrase, meaning to understand.

• skilja = understand
• að skilja = to understand

After hjálpa, Icelandic commonly uses að + infinitive:

• hjálpa mér að lesa = help me to read
• hjálpa mér að skrifa = help me to write
• hjálpa mér að skilja = help me to understand

So að here works much like English to in helps me to understand.

Textann is the definite form of texti and it is in the accusative singular, because it is the direct object of skilja.

Breakdown:

• texti = text
• textann = the text (accusative singular)

In the phrase:

• að skilja textann = to understand the text

the verb skilja takes a direct object, and that object is in the accusative.

So the sentence has:

• subject: athugasemdin
• verb: hjálpar
• indirect/dative object: mér
• infinitive phrase: að skilja textann betur

Betur means better.

It is the comparative form of vel (well), but in Icelandic betur is also often used where English would simply say better after a verb like understand.

So:

• skilja textann betur = understand the text better

Even though English says better here, Icelandic is using an adverbial comparative form.

Related forms:

• vel = well
• betur = better
• best = best

A useful way to see it is:

• Athugasemdin = subject
• í bókinni = prepositional phrase describing where the comment is
• hjálpar = main verb
• mér = dative object
• að skilja textann betur = infinitive phrase explaining what it helps me do

So the structure is roughly:

[The comment in the book] [helps] [me] [to understand the text better].

This is fairly close to English word order, which makes the sentence easier than some other Icelandic sentences.

Most naturally, í bókinni describes athugasemdin:

• Athugasemdin í bókinni = the comment in the book

So the meaning is that the comment/note is in the book.

It is not most naturally understood as helps me in the book. Icelandic, like English, lets this phrase sit after the noun it describes.

Because Icelandic is being specific about both nouns:

• athugasemdin = the comment
• textann = the text

This suggests we are talking about a particular comment and a particular text, not just any comment and any text.

If they were indefinite, the sentence would look different, for example:

• Athugasemd í bók hjálpar mér ... would sound much less natural in this context and much less specific.

In normal Icelandic, definiteness is often shown by attaching the article to the noun, as seen here.

Yes, depending on context.

Athugasemd can mean things like:

• comment
• remark
• note
• sometimes even annotation

So if this is about a printed explanatory note in a book, note may sound more natural in English:

• The note in the book helps me understand the text better.

If it is more like an observation or comment, then comment works well too. The exact best translation depends on context.

Yes. The pattern is very natural:

• hjálpa einhverjum að + infinitive

Examples:

• Hún hjálpar mér að læra. = She helps me study.
• Þetta hjálpar okkur að vinna hraðar. = This helps us work faster.
• Athugasemdin hjálpar mér að skilja. = The comment helps me understand.

So this sentence is a very useful model for making similar sentences of your own.