Mater filio ignoscit, si crimen suum aperte fatetur.

Because mater is in the nominative singular, which is the usual case for the subject.

Even though mater does not have the very common -a nominative ending, it is still nominative. It is a third-declension noun:

• mater = mother
• nominative singular: mater

The verb ignoscit is third person singular, so it matches mater: the mother forgives.

Because the verb ignoscere takes the dative of the person being forgiven.

So Latin says, literally, something like:

• mater filio ignoscit = the mother grants forgiveness to the son

This is different from English, where forgive usually takes a direct object: the mother forgives the son.

So:

• filio = to/for the son = dative singular

Crimen is accusative singular.

That is because it is the direct object of fatetur:

• fatetur crimen = he admits/confesses the crime

The noun crimen, criminis is a neuter third-declension noun, and its nominative and accusative singular are both crimen.

Because suum is the reflexive possessive adjective, meaning his own / her own / their own.

Here the understood subject of fatetur is the same person as filio in the main idea: the son is the one admitting the crime. So Latin uses suum to show that it is his own crime.

• crimen suum = his own crime

If Latin wanted to say someone else’s crime, it would more likely use eius:

• crimen eius = his/her crime (not necessarily his/her own)

Suum agrees with crimen, not with the person who owns it.

That is an important Latin point: a possessive adjective agrees with the thing possessed in gender, number, and case.

So here:

• crimen = neuter singular accusative
• suum = neuter singular accusative

Even though the owner is a male person in the meaning, the form is suum because it matches crimen, not filio.

Because fateor, fateri is a deponent verb.

Deponent verbs:

• have passive-looking forms
• but active meanings

So:

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

This is very common in Latin and often surprises English speakers at first.

Fatetur is:

• present tense
• indicative mood
• third person singular
• from the deponent verb fateor, fateri

So it means:

• he admits
• she admits

In this sentence, the understood subject is the son.

Because Latin often leaves out subject pronouns when they are not needed.

The ending of the verb already tells you the person and number:

• fatetur = he/she admits

And from the context, we understand that the person is the son. Latin does not need to say is or ille here unless it wants extra emphasis.

Aperte is an adverb, and it means openly, plainly, or frankly.

It modifies fatetur:

• aperte fatetur = admits openly

English speakers can think of it as answering the question how?

• How does he admit it?
• Openly

Because Latin often uses the present indicative for a general condition or a statement of what happens whenever the condition is met.

So this sentence is not necessarily describing one single event happening right now. It can mean something like:

• The mother forgives her son if he openly admits his crime

That is a normal, general statement.

It is a simple condition introduced by si, meaning if.

Both verbs are in the indicative, which is very normal for a straightforward condition:

• Mater filio ignoscit
• si crimen suum aperte fatetur

So the sense is simply:

• if he admits his crime openly, the mother forgives him

There is nothing especially hypothetical or contrary-to-fact here. It is just a plain if clause.

The word order is less rigid in Latin than in English because the endings show each word’s job in the sentence.

This order is natural and clear:

• Mater = subject first
• filio = the person forgiven
• ignoscit = verb
• then the si clause

But Latin could move words around for emphasis without changing the basic meaning, as long as the forms stay the same.

For example, crimen suum is kept together neatly, and aperte is placed next to fatetur, which makes good sense stylistically.

That is just a natural way to arrange the sentence: first the main statement, then the condition.

Latin could also put the si clause first:

• Si crimen suum aperte fatetur, mater filio ignoscit.

Both are possible. The version you have simply begins with the main idea and then adds the condition.