Poeta in theatro carmen breve cantans a turba libenter auditur.

Because the main verb, auditur, is passive: is heard.

In a passive sentence, the person or thing receiving the action becomes the subject and therefore goes in the nominative case. So:

• poeta = the poet (subject, nominative)
• auditur = is heard

If Latin wanted to say the crowd hears the poet in the active voice, it would be something like:

• turba poetam audit

There, poetam would be accusative because it would be the direct object.

Auditur is the 3rd person singular present passive indicative of audio, audire, meaning to hear.

So:

• audit = he/she/it hears
• auditur = he/she/it is heard

Since poeta is singular, the verb is also singular: auditur.

Because in a passive sentence, the doer of the action can be expressed with a/ab + ablative. This is called the ablative of agent.

So:

• a turba = by the crowd

Here the crowd is the agent, the one doing the hearing.

A helpful contrast:

• Poeta auditur a turba = The poet is heard by the crowd
• Turba poetam audit = The crowd hears the poet

Because when the agent is a person or persons, Latin normally uses a/ab + ablative in passive constructions.

Since turba means a crowd of people, Latin treats it as an agent, so a turba is expected.

By contrast, with an impersonal means or instrument, Latin often uses the plain ablative without a/ab:

• gladio vulneratur = he is wounded by a sword

But:

• a milite vulneratur = he is wounded by a soldier

Cantans is the present active participle of canto, meaning singing.

It describes poeta, so the phrase means:

• poeta ... cantans = the poet ... singing

More naturally in English, the whole sentence can be understood as:

• The poet, singing a short song in the theater, is gladly heard by the crowd.

So cantans is acting like an adjective, but with verbal force.

Because Latin is not making singing the main finite verb. The main verb of the sentence is auditur.

Compare:

• cantat = he sings
  This would be a second full verb.
• cantans = singing
  This is a participle, used to describe the poet while the main action is is heard.

So Latin is saying something like:

• The poet, singing a short song, is heard...

rather than:

• The poet sings a short song and is heard...

Because it agrees with poeta, the word it describes.

Poeta is:

• nominative
• singular
• masculine in meaning

So the participle is also nominative singular: cantans.

Present participles in Latin behave like adjectives in agreement, even though they come from verbs.

Because carmen is a neuter noun.

Carmen means song and is the direct object of cantans: the poet is singing a short song. Since carmen is neuter singular, the adjective must agree with it:

• carmen = neuter singular accusative
• breve = neuter singular accusative

In many neuter nouns and adjectives, the nominative and accusative forms are the same. That is why you see breve, not brevem.

Carmen breve is accusative singular, and it depends on cantans.

Even though cantans is a participle, it still keeps its verbal force, so it can take a direct object:

• cantans carmen breve = singing a short song

So the structure is:

• poeta = the poet
• cantans carmen breve = singing a short song

Because in with the ablative usually means in or on in the sense of location.

So:

• in theatro = in the theater

If there were motion into the theater, Latin would usually use in + accusative instead:

• in theatrum = into the theater

Here the idea is location, not motion, so theatro is ablative.

It most naturally describes the scene as a whole, and especially the poet while singing:

• the poet, singing a short song in the theater

But Latin word order is flexible, so a phrase like in theatro can sometimes be understood with the broader action too:

• the hearing happens there as well

In practice, a learner should understand it as a location phrase that fits the whole event, with especially close sense to cantans.

Libenter means gladly, willingly, or with pleasure.

Here it tells us how the crowd hears the poet:

• a turba libenter auditur = he is gladly heard by the crowd

It is an adverb, so it modifies the verb auditur.

Because it modifies the main verb, auditur.

Latin word order is flexible, but words are often placed near the things they most closely relate to. So libenter auditur naturally means:

• is gladly heard

That said, Latin could move libenter elsewhere for style or emphasis.

Because Latin has no articles like English the and a/an.

So:

• poeta can mean a poet or the poet
• turba can mean a crowd or the crowd
• carmen breve can mean a short song or the short song

The context and the translation chosen for the sentence decide which is most natural in English.

Yes. Poeta is a common example of a first-declension noun with masculine meaning.

So although it looks like many feminine first-declension nouns, it usually refers to a male poet and is grammatically treated accordingly in meaning.

This is not unusual in Latin for certain words referring to professions or roles, such as:

• poeta = poet
• agricola = farmer
• nauta = sailor

A very literal breakdown is:

• Poeta = the poet
• in theatro = in the theater
• carmen breve = a short song
• cantans = singing
• a turba = by the crowd
• libenter = gladly
• auditur = is heard

So the sentence is literally something like:

• The poet, in the theater, singing a short song, by the crowd gladly is heard.

That sounds unnatural in English, but it is normal Latin style.

Because Latin relies much more on inflection than on fixed word order.

Even though poeta and cantans belong together, other phrases can be placed between them without causing confusion, because the endings show the relationships.

So Latin can write:

• Poeta in theatro carmen breve cantans...

and the reader still understands that cantans describes poeta.

Yes. Several English versions are possible, depending on style:

• The poet, singing a short song in the theater, is gladly heard by the crowd.
• The poet singing a short song in the theater is heard gladly by the crowd.
• While singing a short song in the theater, the poet is gladly listened to by the crowd.

The last one is slightly freer, because auditur literally means is heard, not specifically is listened to, but English may sometimes prefer that wording.

Yes—this sentence is a nice example of several key Latin features all at once:

• passive verb: auditur
• agent with a/ab + ablative: a turba
• present participle: cantans
• object of the participle: carmen breve
• location with in + ablative: in theatro
• free word order
• no articles

So if the sentence feels dense, that is normal: it combines several common Latin patterns in one line.