Nasza córka siedzi na huśtawce i śmieje się bardzo głośno.

Because córka is a feminine singular noun, and the possessive adjective nasz (our) has to agree with it.

So:

• nasz = masculine singular
• nasza = feminine singular
• nasze = neuter singular / some plural forms

Since córka is feminine, we use nasza córka.

It is in the nominative case because it is the subject of the sentence — the person doing the actions.

In this sentence, nasza córka is the one who:

• siedzi = is sitting
• śmieje się = is laughing

So nominative is the expected case here.

Because na can take different cases depending on meaning.

Here the idea is location: she is sitting on a swing, already there. With location, na usually takes the locative case.

• huśtawka = swing
• na huśtawce = on the swing

If there were motion toward the swing, Polish would often use the accusative:

• usiadła na huśtawkę would actually sound wrong with this verb, but with other motion contexts you do see na + accusative
• more naturally: weszła na huśtawkę = she got onto the swing

So in your sentence, na huśtawce is locative because it answers where?

Huśtawce is the locative singular form of huśtawka.

Basic forms:

• nominative: huśtawka
• locative: na huśtawce

This is a very common pattern for feminine nouns ending in -ka:

• książka → o książce
• ławka → na ławce
• huśtawka → na huśtawce

Siedzi is the 3rd person singular present tense of siedzieć.

It means:

• she is sitting
• or sometimes more generally she sits

In this sentence, it most naturally means is sitting, because the sentence describes what is happening right now.

Conjugation of siedzieć in the present:

• siedzę = I sit / am sitting
• siedzisz = you sit / are sitting
• siedzi = he/she/it sits / is sitting

Polish does not have a separate tense form exactly like the English present continuous.

Instead, the present tense often covers both:

• she sits
• she is sitting

So:

• siedzi can mean sits or is sitting
• śmieje się can mean laughs or is laughing

The context tells you which sounds best in English.

The verb is śmiać się, which means to laugh.

Here, się is part of the verb. It does not literally mean herself in this sentence. You should learn śmiać się as a whole expression.

So:

• śmieję się = I am laughing
• śmiejesz się = you are laughing
• śmieje się = he/she is laughing

Many Polish verbs use się, and sometimes it feels reflexive, but very often it is just part of the standard verb form.

Yes, sometimes się can move, because it often avoids standing in certain positions.

In this sentence, the normal version is:

• Nasza córka siedzi na huśtawce i śmieje się bardzo głośno.

You may also hear:

• Nasza córka siedzi na huśtawce i bardzo głośno się śmieje.

Both are natural. The meaning is the same, but the emphasis changes slightly.

A useful point for learners: się is often flexible, but it still follows certain word-order habits, so it is best at first to memorize common verb phrases such as śmiać się.

Because głośno is an adverb, and it modifies the verb śmieje się.

It tells us how she is laughing:

• głośno = loudly

Compare:

• głośny śmiech = loud laughter
• ona jest głośna = she is loud
• śmieje się głośno = she laughs loudly

So:

• adjective: głośny / głośna / głośne
• adverb: głośno

Bardzo means very. It strengthens the adverb głośno.

So:

• głośno = loudly
• bardzo głośno = very loudly

This is a very common pattern in Polish:

• bardzo dobrze = very well
• bardzo szybko = very quickly
• bardzo cicho = very quietly

Because Polish has no articles.

English says:

• our daughter is sitting on a swing
• our daughter is sitting on the swing

Polish does not normally use separate words for a/an/the. The meaning depends on context.

So:

• na huśtawce can mean on a swing or on the swing

The listener understands from the situation what is meant.

Yes. I means and and joins the two actions done by the same subject:

• siedzi na huśtawce = is sitting on the swing
• śmieje się bardzo głośno = is laughing very loudly

So the sentence says that our daughter is doing both actions.

Yes. Polish word order is more flexible than English word order, because cases and verb forms carry a lot of grammatical information.

The neutral sentence is:

• Nasza córka siedzi na huśtawce i śmieje się bardzo głośno.

But you could also say:

• Nasza córka bardzo głośno śmieje się na huśtawce.
• Na huśtawce siedzi nasza córka i bardzo głośno się śmieje.

These versions shift the emphasis:

• starting with na huśtawce emphasizes the location
• placing bardzo głośno earlier emphasizes how loudly she is laughing

For learners, the original order is a very natural and safe one.

A few key points:

• ó sounds like u
  • córka sounds roughly like CUR-ka
• ś is a soft sh-like sound
  • in huśtawce
  • and in śmieje
• się is usually pronounced roughly like shyeh / syen depending on speech style, but not exactly like English see-eh
• śmieje begins with a soft cluster; roughly SHMYE-ye

Very rough pronunciation guides:

• Nasza córka ≈ NA-sha CUR-ka
• na huśtawce ≈ na hoo-SHTAF-tseh
• śmieje się ≈ SHMYE-ye shyeh

These are only approximations, but they can help at the beginning.

It describes two actions happening at the same time:

1. siedzi na huśtawce = she is sitting on the swing
2. śmieje się bardzo głośno = she is laughing very loudly

Polish often links simultaneous actions this way with i (and). The subject nasza córka applies to both verbs.