Mater dicit pluviam mox desituram esse, et pueri foris ludere poterunt.

Because after dicit, Latin often uses an indirect statement construction.

In an indirect statement:

• the subject of the reported idea goes into the accusative
• the verb goes into an infinitive

So instead of a direct statement like:

• Pluvia mox desinet = The rain will stop soon

Latin reports it as:

• Mater dicit pluviam mox desituram esse = Mother says that the rain will stop soon

Here, pluviam is the subject of the reported clause, but because it is inside an indirect statement, it appears in the accusative.

Desituram esse is the future infinitive of desino.

Latin cannot normally use a regular finite future verb inside this kind of indirect statement. Instead, it uses the future infinitive to show that the action is future relative to the main verb dicit.

So:

• direct: Pluvia mox desinet = The rain will stop soon
• indirect: Mater dicit pluviam mox desituram esse = Mother says that the rain is going to stop soon / will stop soon

The form is built from:

• the future active participle: desitura
• plus esse

Together: desituram esse

Because desituram must agree with pluviam.

The future active participle behaves like an adjective, so it agrees with the noun it goes with in:

• gender
• number
• case

Here:

• pluviam is feminine
• singular
• accusative

So the participle must also be feminine singular accusative:

• desituram

If the subject were masculine, you would get -urum; if neuter, -urum in the neuter form; and so on.

Yes. That is exactly the idea.

English uses that plus a normal clause:

• Mother says that the rain will stop soon

Latin usually does this differently after verbs like say, think, know, hear, and similar verbs. Instead of that + finite verb, it uses:

• accusative subject + infinitive

So:

• Mater dicit pluviam mox desituram esse

literally looks more like:

• Mother says the rain to be about to stop soon

but in normal English we translate it as:

• Mother says that the rain will stop soon

Mox means soon.

It modifies the idea of stopping, so the sense is:

• the rain will soon stop

Latin word order is flexible, so mox can often move around without changing the basic meaning very much. Here it sits naturally inside the indirect statement:

• pluviam mox desituram esse

That placement is perfectly normal.

Because the children’s being able to play is expected to happen after the rain stops.

So Latin uses the future:

• poterunt = they will be able

The logic is:

• Mother says the rain will stop soon,
• and then the boys will be able to play outside.

If Latin used possunt, that would mean they are able now, which would not fit the situation as well.

Because possum takes an infinitive.

So:

• poterunt ludere = they will be able to play

This is just like English:

• can play
• will be able to play

After verbs of being able, wanting, daring, beginning, and similar ideas, Latin often uses an infinitive.

So here:

• pueri = subject
• poterunt = will be able
• ludere = to play

Together:

• the boys will be able to play

Foris here means outside.

So:

• pueri foris ludere poterunt = the boys will be able to play outside

It is an adverb here, telling where the playing happens.

Learners sometimes confuse foris with forms related to door, because historically the word is connected with that idea, but in sentences like this it simply means outside.

Because Latin usually does not need a word corresponding directly to English that in this kind of sentence.

English says:

• Mother says that the rain will stop soon

Latin usually says:

• Mother says the rain to be going to stop soon

That is, Latin prefers the accusative-and-infinitive construction rather than a conjunction meaning that plus a finite clause.

So the lack of a separate word for that is completely normal.

Yes, but it would be a different sentence structure.

A direct quotation or direct statement would look like:

• Mater dicit: Pluvia mox desinet.

That means:

• Mother says: The rain will stop soon.

But the given sentence uses reported speech, not a direct quotation:

• Mater dicit pluviam mox desituram esse.

So both are possible, but they are different constructions.

The sentence has two main parts joined by et:

1. Mater dicit pluviam mox desituram esse
2. et pueri foris ludere poterunt

The first part has:

• a main verb: dicit
• plus an indirect statement: pluviam mox desituram esse

The second part has:

• a new subject: pueri
• a new finite verb: poterunt

So et clearly joins two coordinated statements:

• Mother says that the rain will stop soon,
• and the boys will be able to play outside.

Mater is the subject only of dicit.

The second clause has its own subject:

• pueri

So the structure is:

• Mater dicit ...
• et pueri ... poterunt

That means:

• Mother says ...
• and the boys will be able ...

The subject changes after et, so it is important to notice that pueri is nominative and starts the second clause.

The dictionary form is desino, desinere, destiti, desitum.

The form desituram comes from the future active participle:

• masculine: desiturus
• feminine: desitura
• neuter: desiturum

In the sentence we have the feminine accusative singular:

• desituram

A good way to recognize it is to notice the -ur- element, which often appears in future participles:

• amaturus
• facturus
• venturus
• desiturus

So when you see desituram esse, you should think to be going to stop / to be about to stop.

More literally, the future infinitive often has the sense to be going to or to be about to do something.

So:

• pluviam mox desituram esse

literally is something like:

• the rain to be about to stop soon

But in natural English, the best translation is often just:

• that the rain will stop soon

So both ideas are helpful:

• literal understanding: is going to stop
• natural translation: will stop