Hún tekur illgresi úr beðinu á meðan ég vökva blómin.

Because hún means she, and tekur is the 3rd person singular present form of the verb að taka (to take).

So:

• ég tek = I take
• þú tekur = you take
• hún tekur = she takes

In this sentence, tekur is being used in the sense of takes / removes.

Illgresi means weeds or weed growth.

A useful thing to know is that it often behaves like a collective noun in Icelandic, so even though English usually says weeds in the plural, Icelandic can use illgresi as a singular mass noun meaning weed growth or weeds in general.

Here it is the direct object of tekur, so the sentence literally feels like:

• She removes weed growth from the bed...

But natural English is simply:

• She pulls weeds from the flower bed...

Because the preposition úr means out of / from, and it requires the dative case.

The noun is:

• beð = bed, flower bed, garden bed

With the definite article attached:

• beðið = the bed

But after úr, it must be in the dative:

• úr beðinu = out of the bed / from the bed

So the case change is caused by the preposition úr.

That ending includes the definite article and the dative singular ending.

The base noun is:

• beð = bed

Forms:

• beð = a bed
• beðið = the bed
• beðinu = to/from/in the bed, depending on the preposition and case context

In this sentence, beðinu is dative singular definite because of úr.

One important feature of Icelandic is that the definite article is usually attached to the noun, instead of being a separate word like the in English.

Á meðan means while or during the time that.

It introduces a clause that tells you what is happening at the same time as the main action:

• Hún tekur illgresi úr beðinu = She pulls weeds from the bed
• á meðan ég vökva blómin = while I water the flowers

So á meðan links two simultaneous actions.

That is normal for many Icelandic verbs.

The verb is:

• að vökva = to water

Its 1st person singular present form is also:

• ég vökva = I water

So although vökva is also the infinitive form after að, in this sentence it is clearly a finite verb because it follows ég.

Compare:

• að vökva blómin = to water the flowers
• ég vökva blómin = I water the flowers

Blómin means the flowers.

The noun is:

• blóm = flower

Plural:

• blóm = flowers
• blómin = the flowers

Here it is the direct object of vökva, so it means the flowers that are being watered.

A helpful detail: for this noun, the nominative plural and accusative plural definite forms are the same, so blómin can look unchanged.

Yes, it is understandable and natural enough in context. It means to remove weeds from the bed.

However, Icelandic can also use more specific verbs for pulling weeds, depending on style and speaker. So a learner may also encounter other ways to express to weed or to pull weeds.

In this sentence, taka ... úr ... gives the clear idea of taking something out of somewhere, which works well for removing weeds from the flower bed.

The basic structure is:

• Hún tekur illgresi úr beðinu = main clause
• á meðan ég vökva blómin = subordinate time clause

So the full sentence is:

• She pulls weeds from the bed while I water the flowers.

This order is very natural in Icelandic. You could also put the á meðan clause first:

• Á meðan ég vökva blómin, tekur hún illgresi úr beðinu.

That would mean the same thing, though the punctuation may vary depending on style.

Because Icelandic usually expresses the by attaching it to the end of the noun.

In this sentence:

• beðinu = the bed in the dative
• blómin = the flowers

So instead of saying something like a separate the, Icelandic usually builds definiteness into the noun itself.

This is one of the big differences between English and Icelandic grammar.

Yes. Both are in the present tense:

• tekur = takes / is taking
• vökva = water / am watering

As in English, the simple present in Icelandic can often describe an action happening right now, especially in context. So the sentence can mean:

• She is pulling weeds from the bed while I am watering the flowers.

even though Icelandic uses the ordinary present tense forms.