Hún heldur í reipið og brosir.

Hún is the nominative form, and nominative is used for the subject of the sentence.

Here, she is the one doing the actions:

• heldur
• brosir

So Icelandic uses hún.

By contrast, hana is the accusative/object form, used when her receives an action.

Heldur is the 3rd person singular present tense of halda.

So:

• að halda = to hold
• ég held = I hold
• þú heldur = you hold
• hún heldur = she holds

A learner may notice that the vowel changes from a in halda to e in heldur. That is just part of how this verb is conjugated.

Also, Icelandic verbs agree with person and number, not with gender, so:

• hann heldur
• hún heldur
• það heldur

all use the same verb form.

Because Icelandic often uses the pattern halda í + something when the meaning is hold onto or keep hold of something.

So:

• halda í reipið = hold onto the rope

This is a very common thing in Icelandic: a verb and a preposition go together as a fixed pattern.

It is useful to learn halda í as a unit, not just halda by itself.

A related pattern you may also meet is halda á, which often means hold/carry in one’s hands. So the preposition matters.

Because reipið means the rope, while reipi means a rope or just rope.

Icelandic usually adds the definite article as an ending instead of using a separate word like English the.

So:

• reipi = rope / a rope
• reipið = the rope

The ending -ið here is the definite article for this neuter singular noun.

In the expression halda í, the noun after í is normally in the accusative.

So the phrase is understood as:

• halda í reipið

However, with this particular noun, you do not see a visible difference in the form, because reipið is the same in nominative and accusative singular.

So even though the case is accusative here, the word still looks like reipið.

Because the same subject applies to both verbs.

So Icelandic, like English, can say:

• Hún heldur í reipið og brosir.

That means:

• She holds onto the rope and smiles.

You do not need to repeat hún before brosir, because it is already understood.

Repeating it would usually sound more emphatic or stylistically heavier:

• Hún heldur í reipið og hún brosir.

That is possible, but the version without the second hún is more natural here.

Brosir is the 3rd person singular present tense of brosa.

So:

• að brosa = to smile
• ég brosi = I smile
• þú brosir = you smile
• hún brosir = she smiles

It matches the same subject, hún, just like heldur does.

It can mean either one, depending on context.

The plain present tense in Icelandic can be used:

• for something happening right now
• for something that happens generally/habitually

In a picture description or a scene description, this sentence will very naturally be understood as:

• She is holding onto the rope and smiling.

Context tells you which meaning is intended.

Yes. That would be a more explicitly ongoing/right now way to say it.

The pattern is:

• vera að + infinitive

So:

• Hún er að halda í reipið og brosa.

This stresses that the action is in progress.

But the original sentence,

• Hún heldur í reipið og brosir.

is also completely natural, especially in simple descriptions, captions, and narratives.

A useful thing to notice: after að, you use the infinitive:

• halda
• brosa

not:

• heldur
• brosir

No. It is the same spelling, but not the same function here.

In this sentence, heldur is a verb form from halda.

In other contexts, heldur can be an adverb or part of another expression with meanings like rather, instead, or similar.

So when you see heldur, you have to decide from context whether it is:

• a form of the verb halda
• or a different word with another meaning

Here it is definitely the verb.

A rough English-friendly approximation is:

• Hún ≈ hoon
• heldur ≈ HEL-dur
• í ≈ ee
• reipið ≈ RAY-pith
• og ≈ og or ok
• brosir ≈ BROH-sir

A few helpful notes:

• ú is a long oo sound
• ei sounds like ay
• ð is like the th in this, though in fast speech it may sound weaker

So very roughly: hoon HEL-dur ee RAY-pith og BROH-sir