Infans aquam e vase fragili effundit, et mater eum monet.

Because infans is in the nominative singular, the case normally used for the subject.

A few helpful details:

• infans is a 3rd-declension noun.
• Its nominative singular is infans.
• The verb effundit is 3rd person singular, so it matches a singular subject: the infant.

In the second clause, mater is likewise nominative singular and is the subject of monet.

Because aquam is the direct object of effundit.

The verb effundere means to pour out / spill, and the thing being poured out is put in the accusative case. So:

• aqua = water
• aquam = water as the direct object

In other words, the infant is doing the action, and the water is what gets spilled.

Because e/ex means out of or from within, and it regularly takes the ablative case.

Here the water is coming out of the inside of the vessel, so e vase is exactly what you would expect.

• e/ex = out of, from
• vase = ablative singular of vas

So e vase means out of the vessel.

E and ex mean the same thing. Latin uses both forms of the preposition.

A common tendency is:

• e before many consonants
• ex often before vowels or h

But this is not an absolute rule, and both forms can appear in good Latin. In this sentence, e vase is perfectly normal.

Because the preposition e/ex takes the ablative.

So:

• vas = nominative singular, vessel
• vase = ablative singular, out of the vessel

This is one of the most common things to learn in Latin: many prepositions require a specific case, and e/ex requires the ablative.

Because fragili must agree with vase in case, number, and gender.

• vas is neuter singular
• vase is ablative singular
• so the adjective must also be ablative singular neuter: fragili

That is why Latin says:

• e vase fragili = out of a fragile vessel

If it were nominative or accusative neuter singular, you would expect fragile, but here the phrase is ablative because of e.

Because eum is the direct object of monet.

The mother is warning or admonishing him, so Latin uses the accusative:

• is = he
• eum = him

So:

• mater eum monet = the mother warns him

This is the same basic idea as aquam with effundit: the verb acts on a direct object, so the object is accusative.

It refers to infans.

So the structure is:

• Infans ... effundit = the infant spills ...
• et mater eum monet = and the mother warns him

Because eum is masculine singular, it tells you that infans is being understood here as masculine: the baby/child is a boy in this sentence.

Yes. Infans can refer to either a male or a female infant/child, depending on context.

By itself, infans does not force one gender in meaning. But in this sentence, the pronoun eum is masculine, so the infant is being treated as male.

If the infant were female, you would expect eam instead:

• mater eam monet = the mother warns her

Monet comes from monere, which can mean:

• warn
• advise
• admonish
• sometimes remind

In this sentence, warns or admonishes fits well.

Grammatically, monet is:

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

So it means she warns or the mother warns.

Both verbs end in -t, which marks 3rd person singular in the present active indicative.

So:

• effundit = he/she/it spills, pours out
• monet = he/she/it warns

Latin verb endings often tell you the person and number even without a subject pronoun. In this sentence, the nouns infans and mater are stated explicitly, so the meaning is especially clear.

Latin word order is much more flexible than English word order because case endings show how the words function.

This sentence uses a very natural Latin arrangement:

• Infans aquam e vase fragili effundit
• et mater eum monet

A few things to notice:

• the direct object aquam comes before the verb
• the prepositional phrase e vase fragili sits near the object/verb
• the verb often comes at or near the end of the clause

Latin could rearrange many of these words without changing the basic meaning, though the emphasis might change.

Because classical Latin does not have articles like English the, a, or an.

So a noun like infans can mean:

• an infant
• the infant

and mater can mean:

• a mother
• the mother

The context tells you which is most natural in translation.