A gazdaság fontos.

Here a is the definite article, so it means the.

Hungarian has:

• a / az = the
• egy = a / an

So A gazdaság fontos means The economy is important.

Hungarian uses:

• a before a consonant sound
• az before a vowel sound

Since gazdaság starts with g, which is a consonant, the correct form is a: a gazdaság.

Compare:

• a ház = the house
• az autó = the car

In Hungarian, the verb to be is usually left out in the present tense when the subject is third person and the sentence simply says what something is or what it is like.

So:

• A gazdaság fontos = The economy is important

Literally, it looks like The economy important, but in Hungarian that is completely normal.

Compare:

• Én fontos vagyok = I am important
• Te fontos vagy = You are important
• A gazdaság fontos = The economy is important

Because fontos is the predicate adjective here. It is not directly attached to the noun the way important is in an important economy. Instead, it is saying something about the subject.

So:

• A gazdaság fontos = The economy is important

But:

• a fontos gazdaság = the important economy

In other words:

• before the noun: the adjective modifies the noun directly
• after the noun: the adjective is part of the statement about the noun

Yes. Fontos a gazdaság is grammatical, but the word order changes the emphasis.

• A gazdaság fontos is a more neutral statement.
• Fontos a gazdaság puts more focus on fontos: The economy is important / It is the economy that is important.

Hungarian word order is often influenced by focus and emphasis, not just grammar.

Because it is in the basic subject form, called the nominative. In Hungarian, the nominative usually has no special ending.

Here, gazdaság is the subject of the sentence, so the plain dictionary form is used:

• gazdaság = economy

If it had a different role in the sentence, it could take an ending:

• gazdaságot = the economy as a direct object
• gazdaságban = in the economy
• gazdaságról = about the economy

A rough pronunciation is:

[ˈɒzdɒʃaːɡ ˈfontoʃ]? Actually, more accurately for the whole phrase: [ɒ ˈɡɒzdɒʃaːɡ ˈfontoʃ]

A simple English-friendly approximation is:

aw GOZ-daw-shaag FON-tosh

A few useful points:

• Stress is on the first syllable of each word.
• s in Hungarian is pronounced like English sh.
• á is a long vowel.
• The Hungarian a sound is not like English cat; it is more open and back.

So:

• gazdaság sounds roughly like GOZ-daw-shaag
• fontos sounds roughly like FON-tosh

No. Hungarian does not have grammatical gender like many European languages do.

So:

• gazdaság is not masculine, feminine, or neuter
• fontos does not change for gender
• the article does not change for gender either

That makes sentences like this simpler than in many Indo-European languages.

Yes. Depending on context, gazdaság can also refer to things like a farm, an estate, or an economic unit/business operation. However, in many common contexts it means economy.

So this sentence could theoretically be understood differently in another context, but if the meaning shown to you is The economy is important, then that is the intended reading here.