Cum pater domum rediit, filia ei epistulam ostendit.

Here cum means when.

In Latin, cum can introduce different kinds of clauses:

• when
• since
• although

In this sentence, it introduces a simple time clause: When the father returned home, the daughter showed him a letter.

Because it is just stating a straightforward event in time, Latin uses cum with the indicative here, not the subjunctive.

So:

• cum pater domum rediit = when the father returned home

Latin often uses domum by itself to mean homeward or to home.

This is a special idiomatic use of an accusative of motion toward:

• domum = home
• Romam = to Rome
• rus / rurum have similar special patterns in some contexts

So:

• pater domum rediit = the father returned home

English needs to or just says returned home, but Latin does not need a preposition here.

Rediit is:

• 3rd person singular
• perfect active indicative
• from redeō, redīre, rediī/rediit = to go back, return

So rediit means:

• he returned
• or he has returned, depending on context

In this sentence, the natural translation is returned.

Because both nouns are in the nominative singular, which is the usual case for the subject.

• pater = father → nominative singular
• filia = daughter → nominative singular

So the sentence has two clauses:

1. cum pater domum rediit = when the father returned home
2. filia ei epistulam ostendit = the daughter showed him a letter

Latin often changes subjects from one clause to another without needing extra words like English sometimes does.

Ei is dative singular of the pronoun is, ea, id.

Here it means:

• to him
• or more naturally in English, just him

With the verb ostendere (to show), Latin often uses:

• the thing shown in the accusative
• the person shown to in the dative

So:

• epistulam = the letter (thing shown)
• ei = to him (person receiving the showing)

Thus:

• filia ei epistulam ostendit = the daughter showed him a letter

Because it is the direct object of ostendit.

The verb ostendere means to show. The thing being shown is put in the accusative.

So:

• epistula = letter (nominative)
• epistulam = letter as direct object (accusative)

In this sentence, the daughter is showing the letter, so Latin uses epistulam.

Ostendit is:

• 3rd person singular
• perfect active indicative
• from ostendō, ostendere, ostendī, ostentum = to show

Here it means:

• she showed

Because the subject is filia, we translate it as she showed or the daughter showed.

Notice that ostendit can also be a present tense form in some contexts (he/she shows) for certain verbs, but here the sentence clearly uses it as a perfect: the action happened after the father came home.

Both actions are presented as completed past events:

• rediit = returned
• ostendit = showed

This is very common in narrative Latin. The perfect tense often tells the main sequence of events:

1. the father returned home
2. the daughter showed him a letter

English usually also uses the simple past here.

Classical Latin has no articles.

So a noun like pater can mean:

• the father
• a father
• sometimes just father, depending on context

Likewise:

• filia = the daughter or a daughter
• epistulam = a letter or the letter

The context tells you what is most natural. In this sentence, English usually says:

• When the father returned home, the daughter showed him a letter.

But in another context, the letter might also be possible.

Latin word order is more flexible because the endings show each word’s role.

English depends heavily on word order:

• The daughter showed him a letter

Latin can move words around more freely:

• filia ei epistulam ostendit
• epistulam filia ei ostendit
• ei filia epistulam ostendit

All of these can mean basically the same thing, though the emphasis may shift.

In your sentence, the order is quite natural:

• filia first introduces the subject of the main clause
• ei comes early because it is a short pronoun
• epistulam comes before the verb
• ostendit finishes the clause, which is very common in Latin

Grammatically, ei just means to him or to her depending on context, so by itself it could refer to some previously mentioned person.

But in this sentence, the natural reference is pater:

• When the father returned home, the daughter showed him a letter.

So learners should understand ei here as referring back to pater.

Yes. The cum clause comes first:

• Cum pater domum rediit, ...

Latin often puts a subordinate clause like this before the main clause to set the scene first. English does this too:

• When the father returned home, the daughter showed him a letter.

Latin could place the main clause first and the cum clause later, but the version you have is very natural and common.

Because filia is nominative singular of the first-declension noun filia, filiae.

Compare:

• filia = daughter / the daughter
• filiae = daughters or sometimes of the daughter, depending on case and context

Here the verb ostendit is also singular, which confirms that the subject is one daughter:

• filia ... ostendit = the daughter showed