A fürdőruha az öltözőben van.

A word-by-word breakdown is:

• A = the
• fürdőruha = swimsuit / bathing suit
• az = the
• öltözőben = in the changing room / in the dressing room
• van = is

So the structure is basically:

• A fürdőruha = the swimsuit
• az öltözőben van = is in the changing room

Because Hungarian uses the definite article with both definite noun phrases:

• A fürdőruha = the swimsuit
• az öltözőben = in the changing room

This is normal in Hungarian, just as in English you would also say the swimsuit and the changing room.

Hungarian has two forms of the definite article:

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

Since öltöző begins with the vowel ö, the correct form is az:

• a fürdőruha
• az öltözőben

This is similar to English a and an, although the Hungarian article still means the, not a/an.

Hungarian often uses case endings where English uses prepositions.

So instead of:

• in
  • changing room

Hungarian says:

• öltöző
  • -ben

giving:

• öltözőben = in the changing room

This ending is called the inessive case, and it expresses being inside something.

This is due to vowel harmony, a major feature of Hungarian.

The ending meaning in has two common forms:

• -ban
• -ben

Words with front vowels usually take -ben, and words with back vowels usually take -ban.

Since öltöző contains front vowels (ö, ő), it takes:

• öltözőben

A back-vowel example would be:

• házban = in the house

It is a compound noun:

• fürdő = bathing, swimming, bath
• ruha = clothes / garment

So fürdőruha literally means something like bathing clothing, but the natural English translation is swimsuit or bathing suit.

Hungarian makes compounds very freely, so long words like this are common.

That is a very common and very good question.

Hungarian often omits van in the present tense when one noun or adjective is simply identified with another:

• A lány okos. = The girl is smart.
• Ő tanár. = He/She is a teacher.

But in location sentences, van is usually required:

• A fürdőruha az öltözőben van. = The swimsuit is in the changing room.

So here van stays because the sentence tells you where something is.

Hungarian word order is more flexible than English word order, and it often reflects topic and focus rather than a fixed subject-verb-object pattern.

In this sentence:

• A fürdőruha is the topic, what we are talking about.
• az öltözőben van gives the information about it.

Putting van at the end is very natural in a neutral statement like this.

English has to say:

• The swimsuit is in the changing room.

Hungarian often prefers:

• The swimsuit / in the changing room / is

Yes. That is a correct sentence too, but the emphasis changes.

• A fürdőruha az öltözőben van.
  Neutral: we are talking about the swimsuit, and saying where it is.

• Az öltözőben van a fürdőruha.
  This puts more emphasis on the changing room as the location, as if answering Where is the swimsuit?

So both are possible, but they are not used in exactly the same context.

A few helpful points:

• Stress in Hungarian is always on the first syllable.
• ü and ö are front rounded vowels, somewhat similar to sounds in German or French.
• ő is a long version of ö.

Very rough pronunciation guides:

• fürdőruha ≈ FÜR-dur-roo-ha
• öltözőben ≈ UL-tuh-zur-ben or ERL-tuh-zur-ben, depending on your accent and approximation

These are only rough guides. The most important things for learners are:

• stress the first syllable
• notice that ő is long
• pronounce ö/ő and ü differently from plain o and u

Hungarian has no grammatical gender. Nouns are not masculine, feminine, or neuter.

So fürdőruha is just a noun meaning swimsuit. You do not have to memorize a gender for it, and articles do not change for gender either.

That is one thing English speakers often find refreshingly simple about Hungarian.

It can have a small range of related meanings depending on context:

• changing room
• dressing room
• sometimes locker room

The exact best English translation depends on the situation. In a swimming-pool context, changing room is usually the most natural choice here.

Sometimes Hungarian can omit articles, but not in the same way English does.

In this sentence, the articles make the nouns definite and specific:

• A fürdőruha = the swimsuit
• az öltözőben = in the changing room

If you removed them, the sentence would sound different and less natural in most normal contexts. For a learner, it is best to keep the articles here.