Eftir því sem vaxtarskilyrðin verða betri vex basilíkan hraðar.

Eftir því sem ... is a fixed expression that means something like the more ..., as ..., or the ... the ... in English.

So the whole sentence has the pattern:

• Eftir því sem X verður betri, Y vex hraðar
• The better X gets, the faster Y grows

It introduces a relationship where one thing changes together with another.

A very close English pattern is:

• The better the growing conditions become, the faster the basil grows.

Not quite.

• betri is the comparative form of an adjective: góður → betri
  It describes the noun vaxtarskilyrðin (the growing conditions).

• hraðar is the comparative form of an adverb: hratt/hraður → hraðar
  It describes the verb vex (grows), so it means more quickly / faster.

So:

• vaxtarskilyrðin verða betri = the growing conditions become better
• basilíkan vex hraðar = the basil grows faster

A useful way to remember this:

• adjectives describe nouns
• adverbs describe verbs

Because verða means become, while vera means be.

So:

• vaxtarskilyrðin eru betri = the growing conditions are better
• vaxtarskilyrðin verða betri = the growing conditions become better

In this sentence, the idea is that as the conditions improve, the basil grows faster. That is why verða is a good choice.

This is because of Icelandic V2 word order (verb-second).

The sentence begins with a fronted clause:

• Eftir því sem vaxtarskilyrðin verða betri

After that opening element, the finite verb of the main clause must come next:

• vex

And then the subject follows:

• basilíkan

So the word order is:

• [fronted clause] + [verb] + [subject] + ...

That is why you get:

• Eftir því sem vaxtarskilyrðin verða betri vex basilíkan hraðar.

If the main clause stood alone, it would normally be:

• Basilíkan vex hraðar.

This is a very common feature of Icelandic syntax.

It is a compound noun:

• vöxtur = growth
• vaxtar- = a compound form meaning of growth / growth-
• skilyrði = conditions

So vaxtarskilyrði means growth conditions or growing conditions.

The ending -in makes it definite:

• vaxtarskilyrði = growth conditions
• vaxtarskilyrðin = the growth conditions

Also notice that skilyrði is a neuter noun that is very often used in the plural when talking about conditions in general.

The -in is the suffixed definite article, meaning the.

In Icelandic, the is usually attached to the end of the noun instead of standing as a separate word.

So:

• skilyrði = conditions
• skilyrðin = the conditions

Since this noun is plural here, the whole thing means the growing conditions.

This is very typical in Icelandic:

• hús = house
• húsið = the house
• börn = children
• börnin = the children

Again, this is the suffixed definite article.

• basilíka = basil
• basilíkan = the basil

The ending -n here means the.

In context, Icelandic often uses the definite form when talking about a particular plant or the plant as the thing being discussed. So basilíkan vex hraðar means the basil grows faster.

betri is the comparative form of góður (good).

The three basic degrees are:

• góður = good
• betri = better
• bestur = best

In this sentence, betri agrees with vaxtarskilyrðin.

A learner should mainly notice that betri is an irregular comparative, just like English good → better.

So Icelandic is actually similar to English here:

• good → better
• góður → betri

Here hraðar is a comparative adverb, meaning more quickly or faster.

It comes from hratt (quickly / fast):

• hratt = quickly
• hraðar = more quickly / faster
• hraðast = fastest in adverbial use

In the sentence, it modifies the verb vex:

• vex hraðar = grows faster

Even though English often uses faster for both adjective and adverb, Icelandic still distinguishes the grammatical role.

Because vaxa (to grow) is an irregular verb.

Its present tense singular form is:

• ég vex = I grow
• þú vex(t) = you grow
• hann/hún/það vex = he/she/it grows

So in this sentence:

• basilíkan vex = the basil grows

This is just something to learn as a verb form. It is not formed in the most predictable way from the infinitive vaxa.

Því is the dative singular form of the pronoun það, but in eftir því sem you should really learn the whole phrase as a set expression.

So although it is possible to analyze it historically and grammatically, for practical learning it is best to treat:

• eftir því sem

as one chunk meaning:

• the more ...
• to the extent that ...
• as ...

In other words, don’t try to build this phrase word by word at first. Learn it as a pattern.

Yes. It functions like a subordinate clause introducing the condition or scale of change.

Then the main clause is:

• vex basilíkan hraðar

So the structure is:

• subordinate clause: Eftir því sem vaxtarskilyrðin verða betri
• main clause: vex basilíkan hraðar

This matters because it helps explain the word order in the main clause: the finite verb vex comes before the subject basilíkan due to Icelandic V2 rules.

Yes. A fairly literal version would be:

• As the growth conditions become better, the basil grows faster.

Or even more literally in structure:

• The better the growth conditions become, the faster the basil grows.

Both are good English renderings. The second one matches the Icelandic comparative pattern more closely.

It is plural here: vaxtarskilyrðin = the growth conditions.

That can be a little confusing because some Icelandic neuter nouns have the same form in singular and plural in the indefinite, but here the meaning is clearly plural, and the definite ending -in gives:

• skilyrðin = the conditions

So the sentence is talking about conditions in general, not one single condition.

A very useful chunk is:

• Eftir því sem ..., ...
• The more/As ..., ...

For example:

• Eftir því sem þú æfir meira verðurðu betri.
  The more you practice, the better you become.

• Eftir því sem veðrið kólnar þarf ég fleiri föt.
  As the weather gets colder, I need more clothes.

So this sentence is good not just for vocabulary, but also for learning a very common Icelandic comparison structure.