Ég þarf að hneppa jakkanum betur, því rennilásinn er bilaður.

Þarf að + infinitive means need to ....

The dictionary form is að þurfa = to need.
Here, þarf is the present-tense form used with ég:

• ég þarf = I need

So Ég þarf að hneppa ... means I need to fasten/button ...

After þurfa, Icelandic normally uses að + infinitive.

So the pattern is:

• þurfa að gera eitthvað = need to do something

That is why you get:

• Ég þarf að hneppa = I need to fasten/button

English does not always use a separate infinitive marker in the same way, so this is something learners have to get used to.

Hneppa means to fasten, do up, button up, or clasp.

With clothing, it often suggests fastening something such as:

• buttons
• snaps
• clasps
• a garment in general

So in this sentence it means something like do the jacket up more securely or button/fasten the jacket better.

In this sentence, jakkanum is in the dative singular definite form.

That happens because Icelandic verbs do not always take an accusative object. Some verbs and expressions require other cases, and hneppa is used here with the garment in the dative.

So you need to learn this as part of the construction:

• hneppa jakkanum

Also, -num here includes the attached definite article, so jakkanum means the jacket in the dative.

Because betur is an adverb, while betri is an adjective.

Here it describes how the speaker needs to fasten the jacket, so Icelandic uses the adverb:

• hneppa ... betur = fasten ... better / more properly

Compare:

• betri jakki = a better jacket → adjective
• hneppa jakkanum betur = fasten the jacket better → adverb

Also, betur is the comparative form of vel:

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

Here því means because.

It introduces the reason:

• ..., því rennilásinn er bilaður.
• ..., because the zipper is broken.

You may also see því að, which means the same thing. In many sentences, því on its own is perfectly normal.

Icelandic very often forms compounds as a single word, and rennilás is one of them.

• rennilás = zipper
• rennilásinn = the zipper

The ending -inn is the attached definite article, which is how Icelandic usually says the.

So instead of a separate word like English the zipper, Icelandic often puts the article onto the noun itself:

• rennilás = zipper
• rennilásinn = the zipper

Rennilásinn is in the nominative singular definite.

That is because it is the subject of the clause:

• rennilásinn er bilaður = the zipper is broken

In other words, it is the thing that is broken, so it appears in the nominative.

Bilaður means broken, out of order, or not working properly.

It comes from the verb að bila, which means to break down or to malfunction.

The ending -ur is there because bilaður agrees with rennilásinn, which is:

• masculine
• singular
• nominative

So the adjective must match that noun.

For comparison:

• masculine: bilaður
• feminine: biluð
• neuter: bilað

Because hneppa is broader than just zip up. It means fasten / do up.

So the idea is: since the zipper does not work, the speaker needs to fasten the jacket some other way, or more carefully.

In natural English, that might come across as:

• I need to fasten the jacket better, because the zipper is broken.
• I need to button the jacket up better, because the zipper is broken.

So the broken zipper explains why the speaker has to secure the jacket differently or more carefully.

Because því introduces a subordinate clause giving the reason.

The sentence is split into:

• main clause: Ég þarf að hneppa jakkanum betur
• reason clause: því rennilásinn er bilaður

Icelandic punctuation often uses a comma before clauses like this, especially when a reason or explanation follows.