Mater gaudet, quod filia veritatem aperte fatetur.

Here quod means because. It introduces the reason why the mother is glad:

• Mater gaudet = The mother rejoices / is glad
• quod filia veritatem aperte fatetur = because the daughter openly admits the truth

Latin quod can sometimes also mean that, but in this sentence it is most naturally causal: because.

Because the subject is Mater, which is singular:

• mater = mother
• gaudet = she rejoices / is glad

So the verb agrees with a singular subject.

Mater is nominative singular, so it is the subject of gaudet.

Its basic dictionary form is also mater, meaning mother. This is a third-declension noun, so its nominative singular does not have the very obvious -a ending that many first-declension nouns do.

Filia is nominative singular. It is the subject of the verb fatetur inside the quod clause.

So the sentence has two clauses, each with its own subject:

• main clause: Mater gaudet
• subordinate clause: quod filia veritatem aperte fatetur

Even though English sometimes does not make this feel very separate, Latin does: filia is the one doing the admitting, so it must be nominative.

Because veritatem is the direct object of fatetur.

• veritas = truth
• veritatem = accusative singular, the truth

The daughter is admitting the truth, so the thing being admitted is put in the accusative.

Because fatetur is from a deponent verb.

Deponent verbs:

• have passive-looking forms
• but active meanings

So:

• fatetur looks like a passive form
• but means she admits / confesses, not she is admitted

The dictionary form is fateor, fateri, fassus sum = admit, confess.

Aperte is an adverb meaning openly, frankly, or plainly.

It modifies fatetur, telling us how the daughter admits the truth:

• fatetur = admits
• aperte fatetur = admits openly

It comes from apertus (open), but here the adverb form is used.

Latin word order is much freer than English word order. Very often, Latin puts the verb at or near the end of the clause.

So:

• filia veritatem aperte fatetur

is a very natural Latin order.

English usually prefers something like:

• the daughter openly admits the truth

But Latin can move words around for emphasis or style while keeping the meaning clear through case endings.

Yes, quod can sometimes introduce a content clause, especially after verbs of emotion or statements, and then it may be translated that.

So this sentence could be understood as:

• The mother rejoices because the daughter openly admits the truth
• or The mother rejoices that the daughter openly admits the truth

In many classroom contexts, the first translation, because, is preferred here, but both ideas are close.

After a verb like gaudet, Latin often uses a subordinate clause rather than an accusative-and-infinitive construction.

So Latin says:

• Mater gaudet, quod...

rather than something built with an infinitive.

Also, verbs of emotion frequently take clauses expressing the cause or content of the emotion. Using quod here is very natural.

Both are present tense, third person singular:

• gaudet = she is glad / rejoices
• fatetur = she admits / confesses

The present tense here gives a straightforward statement of what is happening or is generally true in the situation.

Here are the main dictionary forms:

• mater, matris = mother
• gaudeo, gaudere, gavisus sum = rejoice, be glad
• quod = because, sometimes that
• filia, filiae = daughter
• veritas, veritatis = truth
• aperte = openly, plainly
• fateor, fateri, fassus sum = admit, confess

Noticing dictionary forms helps you see how the sentence is built from the forms actually used.

Yes—this sentence is useful because it shows several very common Latin features all at once:

1. A main clause plus a subordinate clause

   • Mater gaudet
   • quod filia veritatem aperte fatetur

2. Case tells you the job of a noun

   • mater = subject
   • filia = subject of the subordinate clause
   • veritatem = direct object

3. An adverb modifying a verb

   • aperte modifies fatetur

4. A deponent verb

   • fatetur looks passive, but means active

5. Flexible word order

   • especially the verb at the end of the clause

So even though the sentence is short, it teaches several core patterns of Latin grammar.