Hún tekur líka bakpoka með sér, því vatnsflaskan hennar er stór og nestið er þungt.

Because bakpoki is the dictionary form, the nominative singular. After the verb taka in this sentence, the noun is the direct object, so it goes into the accusative:

• bakpoki = nominative
• bakpoka = accusative

So Hún tekur bakpoka uses the correct object form.

There is no separate word for a/an in Icelandic. Icelandic has no indefinite article.

So:

• bakpoki can mean a backpack or just backpack, depending on context
• bakpokinn means the backpack

In this sentence, bakpoka is indefinite, so it corresponds to a backpack.

Með sér means with her(self) here.

It uses the reflexive pronoun sig/sér/sín, which is used when the object refers back to the subject of the same clause.

• Hún tekur bakpoka með sér = She takes a backpack with her

The form sér is used because með normally takes the dative in this meaning.

A useful contrast:

• með sér = with herself / with her, referring back to the subject
• með hana = with her, but not reflexive in the same way

In Icelandic, possessive words like hennar, hans, and þeirra are very often placed after the noun.

So:

• vatnsflaskan hennar = her water bottle

This word order is very natural in Icelandic. English usually puts the possessive first, but Icelandic often prefers noun + possessive.

Also, hennar does not change form here.

It is a compound word:

• vatn = water
• flaska = bottle
• vatnsflaska = water bottle
• vatnsflaskan = the water bottle

The -s- in the middle is a common linking form in compounds. So literally it is something like water-bottle.

This kind of compounding is extremely common in Icelandic.

Because nestið is the definite form of nesti.

• nesti = a packed lunch / food brought along
• nestið = the packed lunch / the food

Icelandic usually adds the definite article to the end of the noun instead of using a separate word like the.

Since nesti is a neuter noun, the definite ending here is -ið.

Because adjectives in Icelandic must agree with the noun they describe in gender, number, and usually case.

Here:

• vatnsflaskan is feminine singular, so we get stór
• nestið is neuter singular, so we get þungt

So:

• vatnsflaskan hennar er stór = Her water bottle is big
• nestið er þungt = The packed lunch is heavy

This is a very important feature of Icelandic grammar.

Here því means because.

So:

• ..., því vatnsflaskan hennar er stór og nestið er þungt.
• ..., because her water bottle is big and the packed lunch is heavy.

This því is a conjunction introducing a reason.

Learners sometimes notice that því can also appear in other roles in Icelandic, but in this sentence it simply functions as because.

After því, you are in a subordinate clause, so the word order is more like subject + verb:

• því vatnsflaskan hennar er stór

In a main clause, Icelandic often has verb-second word order, but subordinate clauses do not follow that pattern in the same way.

So this is normal:

• Hún tekur líka bakpoka...
• ...því vatnsflaskan hennar er stór...

Líka means also. Its position can vary, and the placement affects emphasis.

In this sentence:

• Hún tekur líka bakpoka means She also takes a backpack

With líka after the verb, the sentence naturally means that taking a backpack is an additional thing she does.

If you move líka, the nuance can shift slightly, so learners should pay attention to where adverbs are placed. But the version in the sentence is completely natural and common.