Dyrygent zaczyna próbę.

Because próbę is in the accusative case, which is used for the direct object of the verb.

• Dictionary form: próba
• Accusative singular: próbę

In Dyrygent zaczyna próbę, the thing being started is the rehearsal, so próba changes to próbę.

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

• książka → książkę
• kawa → kawę
• próba → próbę

Zaczyna is the 3rd person singular present tense form of the verb zaczynać, meaning to begin / to start.

So:

• ja zaczynam = I begin
• ty zaczynasz = you begin
• on / ona / ono zaczyna = he / she / it begins

Since dyrygent is he grammatically, zaczyna means he begins / starts.

Polish word order is fairly flexible, but the most neutral order here is:

• Dyrygent zaczyna próbę.
• subject + verb + object

That is very natural and straightforward.

You can change the order for emphasis, for example:

• Próbę zaczyna dyrygent. = It is the conductor who begins the rehearsal.
• Zaczyna dyrygent próbę. = possible, but less neutral

So the original sentence uses the most standard, unmarked order.

Polish does not have articles like a or the.

So:

• dyrygent can mean a conductor or the conductor
• próba can mean a rehearsal or the rehearsal

You understand which one is meant from context.

That is why Dyrygent zaczyna próbę has no separate words for the.

Dyrygent is a masculine noun.

In this sentence, that matters because the verb form matches a 3rd person singular subject, and in past tense or adjectives you would also see masculine agreement.

For example:

• Ten dyrygent = this conductor
• Dobry dyrygent = a good conductor

Even though the present tense verb zaczyna does not visibly show masculine gender, the noun itself is masculine.

A rough pronunciation guide:

• Dyrygent ≈ duh-RIH-ghent
• zaczyna ≈ za-CHIH-na
• próbę ≈ PROO-beh

A few useful pronunciation points:

• y is not the same as English ee. It is a harder vowel, somewhere like a short central ih sound.
• cz sounds like English ch in chop, but usually a bit harder.
• ó is pronounced like u.
• ę is a nasal vowel, but at the end of a word it is often pronounced approximately like e or em/en depending on speech style and context.

Stress in Polish is usually on the second-to-last syllable:

• dy-RY-gent
• za-CZY-na
• PRÓ-bę

Zaczynać is imperfective.

Its perfective partner is usually zacząć.

This matters because Polish verbs often come in aspect pairs:

• zaczynać = imperfective
• zacząć = perfective

In many everyday present-tense statements like this one, Polish often uses the imperfective form:

• Dyrygent zaczyna próbę.

Very roughly:

• imperfective focuses more on the action/process or a general present situation
• perfective focuses on completion or a single whole event

A related pair:

• Dyrygent zaczyna próbę. = The conductor is beginning / begins the rehearsal.
• Dyrygent zaczął próbę. = The conductor began the rehearsal.

Yes. Próba can also mean attempt or trial, depending on context.

For example:

• To była dobra próba. = That was a good attempt.
• Mamy próbę o szóstej. = We have rehearsal at six.

In Dyrygent zaczyna próbę, the context strongly points to rehearsal, because a conductor naturally starts a rehearsal.

Yes. Rozpoczyna is also correct and means begins / starts.

Compare:

• Dyrygent zaczyna próbę.
• Dyrygent rozpoczyna próbę.

Both are grammatical.
Rozpoczyna can sound a bit more formal or official, while zaczyna is very common and neutral.

You negate the verb with nie:

• Dyrygent nie zaczyna próby.

Notice something important: when the verb is negated, the object often changes case.

Affirmative:

• zaczyna próbę → accusative

Negative:

• nie zaczyna próby → genitive

So:

• Dyrygent zaczyna próbę. = The conductor begins the rehearsal.
• Dyrygent nie zaczyna próby. = The conductor is not beginning the rehearsal.

This genitive after negation is a classic Polish pattern, though in modern Polish there are some contexts where usage can vary.

Because dyrygent is the subject of the sentence, and the subject is normally in the nominative case.

The dictionary form of a noun is usually the nominative singular, and here that is exactly the form needed:

• dyrygent = nominative singular

So:

• Dyrygent = subject
• zaczyna = verb
• próbę = direct object in the accusative

Only próba changes here, because it is the object.

If you want to say The conductors begin the rehearsal, you would say:

• Dyrygenci zaczynają próbę.

Changes:

• dyrygent → dyrygenci = nominative plural
• zaczyna → zaczynają = 3rd person plural
• próbę stays próbę because it is still a singular direct object

So this sentence is a good example of how the verb changes with the subject, while the object keeps the case required by its role in the sentence.