O órgão público fica no centro.

O is the masculine singular definite article, meaning the.

It is used because órgão is a masculine singular noun:

• o órgão = the agency / the body / the organ

In Portuguese, articles are used very often, more often than in English.

Órgão público usually means a public agency, government body, or public institution depending on context.

A few details:

• órgão can literally mean organ in a biological sense, but here it means a body or agency
• público means public

So together:

• órgão público = public agency / government body

In Brazilian Portuguese, this is a common administrative expression.

In Portuguese, adjectives often come after the noun.

So:

• órgão público = literally agency public

This is the normal order in Portuguese.
Sometimes adjectives can come before the noun, but that usually changes the tone or meaning. In this sentence, órgão público is the standard and expected order.

Fica comes from the verb ficar, which can mean different things depending on context.

Common meanings of ficar include:

• to stay
• to remain
• to become
• to be located

In this sentence, fica means is located or is situated:

• O órgão público fica no centro.
• The public agency is located downtown / in the center.

So yes, ficar can mean stay, but not in this sentence.

Portuguese often uses ficar to talk about location, especially when saying where a place or building is situated.

Compare:

• fica no centro = is located downtown / in the center
• está no centro = is in the center
• é no centro is usually not correct for this kind of sentence

So:

• ficar sounds very natural for the location of offices, stores, buildings, and institutions
• estar can also work in many situations, but ficar often emphasizes location more naturally

No is a contraction of:

• em
  • o = no

So:

• em o centro becomes no centro

This means in the or sometimes at the, depending on context.

Other similar contractions:

• na = em + a
• nos = em + os
• nas = em + as

It can mean either one, depending on context.

Very often in Brazilian Portuguese, no centro refers to downtown or the city center.

So this sentence could be understood as:

• The public agency is in the center
• The public agency is downtown
• The public agency is located in the city center

If the broader context is about a city, downtown is often the most natural interpretation.

Órgão has two important accent marks:

• ó shows the stress falls there: ÓR-
• ão is a very common Portuguese ending with a nasal sound

Approximate pronunciation:

• ÓR-gão
• IPA: /ˈɔʁ.ɡɐ̃w̃/ in Brazilian Portuguese

Important points:

• the r is not like an English r
• ão is nasal, which is a sound English does not really have
• the stress is on the first syllable: ÓR

The accent marks are part of correct spelling, so you should always write órgão, not orgao.

The subject is O órgão público.

That is the thing being talked about:

• O órgão público = subject
• fica = verb
• no centro = location phrase

So the structure is:

• [Subject] + [Verb] + [Place]

This is a very common Portuguese sentence pattern.

You can understand it word for word, but a natural English translation may be a little different.

Word-for-word:

• O = the
• órgão público = public body / public agency
• fica = is located / stays
• no centro = in the center / downtown

More natural English versions:

• The public agency is located downtown.
• The government office is in the city center.
• The public body is in the center.

So a literal translation helps with learning, but a natural translation may vary.

Yes, it is natural and correct.

It sounds like a normal sentence you might see in:

• directions
• administrative information
• descriptions of offices or institutions

Depending on context, Brazilians might also say:

• O órgão público está no centro.
• O órgão público fica no centro da cidade.

But O órgão público fica no centro. is perfectly normal.