Cursus pueri matrem terret.

You figure it out mainly from the endings:

• cursus = most likely nominative singular, so it is the subject
• pueri = here genitive singular, meaning of the boy
• matrem = accusative singular, so it is the direct object
• terret = he/she/it frightens, 3rd person singular present

So the structure is:

cursus pueri = the boy's running
matrem = the mother as the object
terret = frightens

Because pueri can be ambiguous by itself. It can mean either:

• of the boy = genitive singular
• the boys = nominative plural

In this sentence, of the boy makes sense because:

• terret is singular, not plural
• matrem is clearly the object
• cursus pueri works naturally as the boy's running

If pueri were the subject meaning the boys, you would usually expect a plural verb, such as terrent.

The verb terret is singular, so it needs a singular subject.

Here, cursus fits that role well: it is functioning as nominative singular.
Meanwhile:

• matrem is accusative, so it is the object
• pueri is genitive, so it depends on cursus

That makes cursus the thing doing the frightening.

Because matrem is the accusative singular form of mater.

Latin uses the accusative case for the direct object, the person or thing directly affected by the verb. Since the mother is the one being frightened, Latin uses matrem.

Compare:

• mater terret = the mother frightens
• matrem terret = he/she/it frightens the mother

The ending shows the job of the word.

No. Cursus is a noun, not a verb.

It comes from the idea of running or a run / movement / course, but grammatically it is a noun. So cursus pueri means something like:

• the boy's running
• the boy's run
• the boy's rushing

English running can look verbal, but here Latin is using a regular noun.

Terret is:

• 3rd person singular
• present tense
• active voice
• indicative mood

It comes from terreo, terrere, meaning to frighten.

So terret means frightens or is frightening, depending on how you want to express it in English.

Because it is singular, it matches a singular subject: cursus.

Because Latin normally does not have articles like English the and a/an.

So a Latin noun like matrem could mean:

• a mother
• the mother

You choose the best English wording from the context. In this sentence, the mother is the most natural translation.

Latin word order is more flexible than English word order because the endings show each word's role.

English depends heavily on position:

• The boy's running frightens the mother

Latin can move words around more freely:

• Cursus pueri matrem terret
• Matrem cursus pueri terret
• Pueri cursus matrem terret

These all can mean the same basic thing, because the endings still show:

• subject
• object
• possession

In this sentence, cursus pueri is simply the Latin way of saying the boy's running, with the genitive pueri following the noun it modifies.

Yes. Cursus can have a range of related meanings, such as:

• running
• a run
• course
• movement
• career or progression in some contexts

But in this sentence, with pueri and terret, the most natural sense is the boy's running or the boy's rush. Context decides which English word sounds best.