Cieszę się, że jutro mamy wolne popołudnie.

Because cieszyć się is a fixed reflexive verb in Polish meaning to be happy / to be glad / to rejoice.

• cieszę by itself would come from cieszyć, which usually means to please or to make someone happy in a different structure.
• cieszę się means I’m glad or I’m happy.

So in this sentence:

• Cieszę się = I’m glad

The się does not translate neatly into English here, but it is required.

Że means that.

It introduces the second clause:

• Cieszę się, że... = I’m glad that...

In English, that is often optional:

• I’m glad that we have a free afternoon tomorrow
• I’m glad we have a free afternoon tomorrow

In Polish, że is very commonly used in this kind of sentence.

Because Polish often drops subject pronouns when they are clear from the verb ending.

• mamy already means we have
• So my mamy is possible, but my is usually unnecessary unless you want emphasis

Compare:

• mamy = we have
• mam = I have
• masz = you have

So jutro mamy wolne popołudnie naturally means tomorrow we have a free afternoon.

In Polish, mieć (to have) is very often used when talking about having time available.

So:

• mamy wolne popołudnie = literally we have a free afternoon

This is a very natural Polish way to express that the afternoon is free or unoccupied.

English can say:

• we have a free afternoon
• our afternoon is free
• we’re free in the afternoon

Polish commonly uses mieć here.

Because wolne must agree with popołudnie in gender, number, and case.

• popołudnie is a neuter singular noun
• So the adjective also takes the neuter singular form: wolne

Examples:

• wolny wieczór = a free evening (masculine)
• wolna sobota = a free Saturday (feminine)
• wolne popołudnie = a free afternoon (neuter)

Here, wolne popołudnie means free afternoon.

It is in the accusative, because it is the direct object of mamy.

• mamy co? → wolne popołudnie

However, for many neuter singular nouns, the nominative and accusative look the same. So:

• nominative: popołudnie
• accusative: popołudnie

That is why there is no visible change in the noun.

Jutro means tomorrow.

It is an adverb of time, so it can stand on its own without a preposition.

• jutro = tomorrow
• dzisiaj = today
• wczoraj = yesterday

So:

• że jutro mamy wolne popołudnie = that tomorrow we have a free afternoon

In natural English, we would usually say:

• that we have a free afternoon tomorrow

But the Polish word order is perfectly normal.

Yes. Polish word order is more flexible than English, as long as the grammar remains clear.

For example, all of these are possible:

• Cieszę się, że jutro mamy wolne popołudnie.
• Cieszę się, że mamy jutro wolne popołudnie.
• Jutro mamy wolne popołudnie, cieszę się. (less neutral, more marked)

The original version sounds very natural and neutral.

In Polish, changing word order often changes emphasis, not the basic meaning.

It means that the afternoon is free, unoccupied, or that you don’t have obligations then.

Depending on context, it can suggest:

• no work
• no classes
• no scheduled plans
• available time to relax or do something else

So it does not necessarily mean a public holiday or a full day off. It specifically refers to the afternoon being free.

Yes, broadly speaking, popołudnie means afternoon.

It refers to the part of the day after midday, before evening.

A useful contrast is:

• rano = in the morning
• przedpołudnie = late morning / before noon
• popołudnie = afternoon
• wieczór = evening
• noc = night

So wolne popołudnie is specifically a free afternoon, not a free evening.

A rough guide is:

Cieszę się ≈ CHESH-eh sheng
że ≈ zheh
jutro ≈ YOO-tro
mamy ≈ MAH-mih
wolne ≈ VOL-neh
popołudnie ≈ po-po-WOOD-nyeh

A few helpful notes:

• ci before a vowel often sounds like soft ch / ć
• sz sounds like sh
• ż sounds like the s in measure
• j sounds like English y
• nie at the end sounds roughly like nye

Polish stress is usually on the second-to-last syllable:

• CIE-szę
• JU-tro
• MA-my
• WOL-ne
• po-po-ŁUD-nie

Yes, but it is not exactly the same in tone.

• Cieszę się, że... = I’m glad that...
• Jestem szczęśliwy/szczęśliwa, że... = I am happy that...

Cieszę się, że... is very common and natural in everyday speech.

Jestem szczęśliwy/szczęśliwa, że... can sound a bit stronger or more emotional, depending on context.

So in this sentence, Cieszę się, że jutro mamy wolne popołudnie is a very natural choice.

Because że introduces a subordinate clause, and in Polish such clauses are normally separated by a comma.

So:

• Cieszę się, że jutro mamy wolne popołudnie.

This is standard Polish punctuation.

A good habit is to expect a comma before że when it means that and introduces a full clause.