Puer piger laborare non vult, sed puella docilis et constans exemplum bonum praebet.

Because Latin often uses an infinitive after verbs like volo (I want, I am willing) to express what someone wants to do.

• vult = he/she wants
• laborare = to work

So laborare vult literally means he wants to work.

This is called a complementary infinitive: the infinitive completes the meaning of the verb vult.

Non negates the verb, so non vult means does not want.

Latin often puts non directly before the word it is negating, especially the verb:

• non vult = does not want

So Puer piger laborare non vult means that the boy is unwilling to work.

Because piger is an adjective agreeing with puer.

Both words are:

• nominative
• singular
• masculine

The boy is the subject of the clause, so both the noun and its adjective must be in the nominative singular masculine.

• puer = boy
• piger = lazy

So puer piger = the lazy boy

The exact ending of the adjective depends on its own declension pattern. The masculine nominative singular of this adjective is piger.

In Latin, adjectives can come before or after the nouns they describe. Both are normal.

So:

• puer piger
• piger puer

can both mean lazy boy

Likewise:

• puella docilis et constans

means a teachable and steadfast girl

Latin word order is much freer than English word order because the endings show the grammatical relationships. Writers often choose word order for style or emphasis rather than strict grammatical necessity.

Because not all Latin adjectives use the -a ending for the feminine.

Many beginners first learn adjectives like:

• bonus, bona, bonum

But docilis and constans belong to different adjective patterns.

• docilis is a third-declension adjective
• constans is also a third-declension adjective

For these adjectives, the masculine and feminine nominative singular are often the same form.

So with puella:

• puella docilis = teachable girl
• puella constans = steadfast girl

Even though puella is feminine, the adjective does not need an -a ending if that adjective belongs to a different declension pattern.

Exemplum bonum is in the accusative singular because it is the direct object of praebet.

• praebet = offers, provides, shows
• What does the girl provide/show? exemplum bonum

So:

• exemplum = accusative singular neuter
• bonum agrees with exemplum, so it is also accusative singular neuter

That is why it is bonum, not bonus or bona.

Because bonum describes exemplum, not puella.

In Latin, an adjective must agree with the noun it modifies, not with some other nearby word.

Here:

• puella is feminine
• exemplum is neuter
• bonum modifies exemplum

So:

• puella docilis et constans
• exemplum bonum

The adjective bonum matches exemplum in:

• gender: neuter
• number: singular
• case: accusative

Literally, praebet means something like provides, offers, or presents.

In this sentence, exemplum bonum praebet is best understood idiomatically as:

• she sets a good example
• or she provides a good example

So even though the basic meaning of praebet is fairly concrete, the whole phrase is a common way to say that someone serves as a model for others.

Both are:

• present tense
• third person singular
• indicative mood

So:

• vult = he/she wants
• praebet = he/she provides / shows / sets

The subjects are singular:

• puer for vult
• puella for praebet

Latin verbs already contain the person and number, so in theory the subject can be omitted:

• laborare non vult = he does not want to work
• exemplum bonum praebet = she sets a good example

But Latin often includes the noun or pronoun anyway for clarity, contrast, or emphasis.

Here the sentence contrasts:

• puer piger
• sed puella docilis et constans

So naming both subjects makes the contrast especially clear.

Sed means but and introduces a contrast between the two clauses.

The contrast is strong:

• the lazy boy does not want to work
• but
• the teachable and steadfast girl sets a good example

So sed marks an opposition between the behavior of the boy and the behavior of the girl.

Classical Latin does not have definite and indefinite articles like English the and a/an.

So:

• puer can mean the boy or a boy
• puella can mean the girl or a girl
• exemplum bonum can mean a good example or the good example, depending on context

English has to choose an article when translating, but Latin usually leaves that idea to context.

Yes, to a large extent. Because Latin uses endings to show grammatical roles, the order can often change without changing the basic meaning.

For example, these would still express essentially the same idea:

• Puer piger non vult laborare, sed puella docilis et constans exemplum bonum praebet.
• Puella docilis et constans exemplum bonum praebet, sed puer piger laborare non vult.

However, changing the word order can change the emphasis or the style. The original order is a natural and clear way to present the contrast.