Az önkormányzat ma nyitva van.

Az is the definite article, so it means the.

Hungarian has two forms of the definite article:

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

Because önkormányzat starts with ö, a vowel, Hungarian uses az önkormányzat.

So:

• a bolt = the shop
• az iskola = the school
• az önkormányzat = the municipal office / the local government

Önkormányzat usually refers to the local government, municipality, or municipal administration.

Depending on context, English may translate it as:

• the local government
• the municipality
• the town hall / municipal office

In this sentence, because it says nyitva van (is open), it most naturally refers to the office or institution that has opening hours, not just the abstract idea of local government.

The stress in Hungarian is always on the first syllable, so this word is stressed as:

ÖN-kor-mány-zat

A rough English-friendly guide would be something like:

URN-kor-maan-y-zot

A few details:

• ö is like German ö or French eu; English does not have an exact match
• á is a long a sound
• ny is like Spanish ñ or the ny sound in canyon

You do not need a perfect English equivalent right away; the important thing is to notice the first-syllable stress and the special vowels.

Ma means today.

Hungarian word order is more flexible than English word order. The sentence:

Az önkormányzat ma nyitva van.

is a very natural, neutral way to say:

The municipal office is open today.

Here the structure is roughly:

• Az önkormányzat = topic, what we are talking about
• ma = time expression
• nyitva van = predicate, what is being said about it

You can move ma, but that changes the emphasis a little:

• Ma az önkormányzat nyitva van. = Today, the municipal office is open.
• Az önkormányzat nyitva van ma. = also possible, but ma sounds a little more like an afterthought

So the given order is simply a normal, neutral order.

For places, shops, offices, and buildings, Hungarian normally uses nyitva van to mean is open in the sense of open for business / not closed.

So:

• A bolt nyitva van. = The shop is open.
• Az önkormányzat ma nyitva van. = The municipal office is open today.

Although nyitott exists, it is not the usual choice for opening hours. Nyitott often means things like:

• opened
• open in a more descriptive or abstract sense
• open-minded, in some contexts

So for everyday opening-hours language, nyitva van is the standard expression.

That is a very common and very good question.

In Hungarian, the 3rd-person singular form of to be is often omitted in the present tense:

• A ház nagy. = The house is big.
• Ő tanár. = He/She is a teacher.

But with forms like nyitva and zárva, Hungarian normally uses van:

• Az ajtó nyitva van. = The door is open.
• A bolt zárva van. = The shop is closed.

So in this sentence, van is the normal and expected form.

You may sometimes see shortened styles without it, especially in signs or very compressed language, but for standard full sentences, nyitva van is the safe pattern to learn.

Nyitva comes from the verb nyit (to open).

It is a -va/-ve participle, a very common Hungarian form. In sentences like this, it expresses a state resulting from an action.

So:

• nyit = to open
• nyitva van = is in an opened/open state

Learners often do best if they simply memorize nyitva van as a unit meaning is open.

Other common examples are:

• zárva van = is closed
• írva van = is written
• ki van nyitva = is opened / is open

Usually, ma nyitva van means that today it is open, often with the sense of according to today's schedule.

It does not necessarily focus on this exact moment. Context decides that.

For example:

• If someone is checking business hours, it means it is open today
• If someone asks whether they can go there now, it may also imply yes, it is open

If you want to make right now more explicit, Hungarian often uses most:

• Az önkormányzat most nyitva van. = The municipal office is open now.

You can change it, but the emphasis changes.

Hungarian word order is strongly connected to information structure: what is the topic, what is being emphasized, and what is already known.

The original sentence:

Az önkormányzat ma nyitva van.

is a neutral statement.

Some alternatives:

• Ma az önkormányzat nyitva van.
  This emphasizes today a bit more.

• Az önkormányzat nyitva van ma.
  Also possible, but ma sounds less central, almost added at the end.

So the words are not completely fixed, but the original version is a very natural basic sentence for a learner to copy.