A kitartás nagyon fontos.

Because Hungarian usually drops the present-tense verb to be in the 3rd person singular and plural when the predicate is a noun or an adjective.

So:

• A kitartás nagyon fontos. = Persistence is very important.

This is normal Hungarian, not an incomplete sentence.

You do use forms of to be in other situations, for example:

• Fontos vagyok. = I am important.
• Fontos vagy. = You are important.
• A kitartás fontos volt. = Persistence was important.
• A kitartás fontos lesz. = Persistence will be important.

So in this sentence, the missing is is completely expected.

Yes, a is the definite article, equivalent to English the.

But Hungarian often uses the definite article where English would use no article, especially with general or abstract ideas.

So:

• A kitartás nagyon fontos.

is most naturally translated as:

• Persistence is very important.

not necessarily:

• The persistence is very important.

Hungarian likes the article here; English usually does not.

A useful comparison:

• A zene fontos. = Music is important.
• A türelem hasznos. = Patience is useful.

Kitartás is a noun. In this sentence it is:

• singular
• nominative (the basic dictionary form)
• the subject of the sentence

There is no extra case ending here.

It is also an abstract noun, meaning something like persistence, perseverance, or endurance, depending on context.

It is related to the verb kitart = to persist / endure / hold out, and the suffix -ás/-és often makes nouns from verbs.

For example, Hungarian often forms nouns like this:

• tanul → tanulás = to study → studying
• olvas → olvasás = to read → reading
• kitart → kitartás = to persist → persistence

Nagyon means very.

It modifies the adjective fontos = important, so:

• nagyon fontos = very important

In Hungarian, adverbs like nagyon normally come before the adjective they modify.

So this is the natural order:

• nagyon fontos

not:

• fontos nagyon in normal neutral speech

A few examples:

• nagyon jó = very good
• nagyon érdekes = very interesting
• nagyon nehéz = very difficult

In this sentence, fontos is a predicate adjective: it tells us what the subject is like.

Hungarian does not have grammatical gender, so there is no masculine/feminine/neuter agreement to worry about.

With a singular subject like kitartás, the adjective stays in its basic form:

• A kitartás fontos.

If the subject were plural, predicate adjectives can show plural:

• A részletek fontosak. = The details are important.

But with this singular abstract noun, fontos is exactly the right form.

Yes, but the emphasis changes.

The sentence you have:

• A kitartás nagyon fontos.

is a very natural, neutral way to say it.

You can also say:

• Nagyon fontos a kitartás.

This puts more emphasis on the idea that it is very important.

You can also say:

• Fontos a kitartás. = Persistence is important.

A useful rule here: nagyon should still stay right before fontos.

So these are good:

• A kitartás nagyon fontos.
• Nagyon fontos a kitartás.

But you would not normally separate nagyon from fontos.

A rough pronunciation guide:

• A = short aw/o sound
• kitartás = KEE-tar-taash
• nagyon = roughly NO-dyon
• fontos = FON-tosh

A more accurate IPA version is:

• A /ɒ/
• kitartás /ˈkitɒrtaːʃ/
• nagyon /ˈnɒɟon/
• fontos /ˈfontoʃ/

A few important pronunciation points:

• Stress is on the first syllable of every Hungarian word.
• s is pronounced like English sh.
  • So fontos ends in -tosh, not -tos.
• gy is a soft sound, roughly like dy in some pronunciations of duke.
• ny is like the ny in canyon.

No. That would be incorrect.

In this kind of sentence, Hungarian does not use van in the present tense.

So the correct form is:

• A kitartás nagyon fontos.

not:

• A kitartás nagyon fontos van.

This is one of the most important differences from English.

However, van is used in other kinds of sentences, especially for location or existence:

• A könyv az asztalon van. = The book is on the table.
• Van időm. = I have time. / There is time for me.

So van is a real verb, but it does not belong in this particular sentence pattern.

You usually use nem.

So:

• A kitartás nem fontos. = Persistence is not important.

If you want to say not very important, you can say:

• A kitartás nem nagyon fontos.

That does not mean the same thing as not important. It means something softer, more like:

• Persistence is not very important.

So:

• nem fontos = not important
• nem nagyon fontos = not very important

Yes, and that can be confusing.

Without the article, Kitartás! is also a common expression meaning something like:

• Hang in there!
• Keep going!
• Stay strong!

But in your sentence:

• A kitartás nagyon fontos.

a kitartás is clearly the noun meaning persistence / perseverance.

So compare:

• Kitartás! = Hang in there!
• A kitartás fontos. = Persistence is important.

Same word, but different use.

Yes, absolutely. It sounds natural and idiomatic.

Its structure is very standard:

• A kitartás = the topic/subject
• nagyon fontos = what is being said about it

This is the kind of sentence Hungarian speakers would really say.

If you want slightly different versions, these are also natural:

• A kitartás fontos.
• Nagyon fontos a kitartás.
• A kitartás rendkívül fontos. = Persistence is extremely important.

So the original sentence is simple, correct, and very usable.