Laufin á plöntunni eru gul, svo ég set hana nær glugganum.

Laufin is the definite neuter plural form of lauf (leaf / leaves).

A useful thing to notice is that lauf is one of those neuter nouns whose indefinite singular and indefinite plural look the same:

• lauf = a leaf
• lauf = leaves
• laufin = the leaves

In this sentence, laufin is the subject: the leaves.

Because á can take either:

• dative for location: on
• accusative for motion onto something

Here the meaning is static location: the leaves are on the plant, not moving onto it. So Icelandic uses the dative:

• á plöntunni = on the plant

Compare:

• Laufin eru á plöntunni. = The leaves are on the plant.
• Ég set lauf á plöntuna. = I put leaves onto the plant.

Plöntunni is the dative singular definite of planta (plant).

Breakdown:

• planta = plant
• plöntu = plant (oblique stem used in several cases)
• plöntunni = to/on/in the plant, depending on the preposition

Here it appears after á in a location meaning, so it must be dative.

Because adjectives in Icelandic agree with the noun in gender, number, and case.

Here the noun is:

• laufin = neuter plural

So the adjective must also be neuter plural:

• gul = yellow, neuter plural

This is also a predicate adjective because it comes after eru (are), and predicate adjectives normally appear in the strong form:

• Laufin eru gul. = The leaves are yellow.

Compare some other forms of gulur:

• masculine singular: gulur
• feminine singular: gul
• neuter singular: gult
• masculine plural: gulir
• feminine plural: gular
• neuter plural: gul

Because Icelandic pronouns follow grammatical gender, not natural gender.

The noun planta is feminine, so when you refer back to it, you use the feminine pronoun:

• hana = her / it (accusative feminine singular)

So:

• ég set hana = I put it

Even though a plant is not female in real life, the noun is grammatically feminine, so Icelandic uses the feminine pronoun.

Because setja takes a direct object, and direct objects are often in the accusative.

The pronoun forms are:

• hún = she / it, nominative
• hana = her / it, accusative

Since the plant is the thing being moved, it is the object of set, so Icelandic uses hana:

• Ég set hana... = I put it...

Nær means nearer / closer.

In this sentence:

• nær glugganum = closer to the window

It is a comparative idea: the plant is being moved to a position closer than before.

So the sentence is not saying only that the plant is near the window, but that it is being moved nearer to it.

Because nær here is followed by the dative, so gluggi (window) appears in the dative singular definite form:

• gluggi = window
• glugga = window (dative singular indefinite)
• glugganum = the window (dative singular definite)

So:

• nær glugganum = closer to the window

Here svo means so, therefore, or as a result.

It connects the two ideas:

• Laufin á plöntunni eru gul = The leaves on the plant are yellow
• svo ég set hana nær glugganum = so I move/put it closer to the window

So svo is showing a consequence: the leaves are yellow, so the speaker changes where the plant is.

Because svo here works like a coordinating conjunction, similar to so in English.

After it, Icelandic starts a new main clause with normal main-clause order:

• ég set hana...

So this is natural:

• ..., svo ég set hana nær glugganum.

If a different structure were used, word order could change, but with svo meaning so / therefore like this, svo ég set... is normal.

Set is the 1st person singular present tense of setja (to put / place / set).

So:

• ég set = I put / I am putting

In context, English may translate it more naturally as I move it closer to the window, even though the Icelandic verb is literally put/place.

For comparison:

• ég set = I put
• ég setti = I put / I placed (past)

Yes, a genitive construction is possible, for example:

• lauf plöntunnar = the plant’s leaves

But laufin á plöntunni is very natural when you are talking about the leaves physically on the plant. It feels concrete and everyday.

So these are close in meaning, but the sentence you were given is very idiomatic and natural.