Mater dicit pueros intra domum manere debere, quia pluvia gravis cadit.

Because after dicit Latin uses indirect statement (also called the accusative-and-infinitive construction).

So instead of saying:

• Mater dicit quod pueri manere debent
  Latin normally prefers:
• Mater dicit pueros manere debere

In this construction:

• the “subject” of the reported statement goes into the accusative → pueros
• the verb of the reported statement goes into the infinitive → manere debere

So pueros means the boys as the subject of the idea being reported, even though it is grammatically accusative.

For the same reason: this is an indirect statement after dicit.

In English we often say:

• Mother says that the boys ought to stay inside the house.

In Latin, after a verb like dicit, the reported action is usually expressed with an infinitive, not a finite verb. So:

• manere = to remain / to stay
• debere = to ought / to have to / to be supposed to

Together, manere debere means to ought to stay or more naturally ought to stay / should stay / have to stay, depending on context.

Because debere is itself a verb that can take another infinitive.

• manere = to stay
• debere = to owe, and from that, to have to / ought to

So:

• manere debere literally = to owe to stay
• idiomatically = to have to stay or to ought to stay

This is similar to English to have to stay:

• stay is the main action
• have to gives the sense of obligation

So in Latin:

• pueros manere debere = that the boys ought to stay

Because Latin usually does not use a word equivalent to English that in this kind of sentence.

English:

• Mother says that the boys should stay inside the house.

Latin:

• Mater dicit pueros intra domum manere debere.

Instead of a separate word meaning that, Latin signals reported speech by using:

• accusative for the subject of the reported statement
• infinitive for its verb

So the structure itself tells you this means says that...

Intra means inside or within, and it takes the accusative case.

So:

• intra domum = inside the house / within the house

That is why domum is accusative.

A learner may expect a preposition meaning in to take the ablative, as in in domo = in the house, but intra is a different preposition and regularly takes the accusative.

Both can refer to being inside a house, but they are not exactly the same.

• in domo = in the house
• intra domum = inside the house / within the house

Intra can feel a bit more emphatic: it stresses being within the interior/bounds of the house.

So in this sentence, intra domum manere gives the idea to stay inside the house, which fits the warning not to go out because of the rain.

Because gravis agrees with pluvia.

• pluvia is feminine singular nominative
• so the adjective must also be feminine singular nominative → gravis

This adjective means heavy, serious, or severe, depending on context.

So:

• pluvia gravis = heavy rain

Yes. Cadit literally means falls.

Latin commonly uses cadere with rain:

• pluvia cadit = rain falls

In natural English we usually just say:

• it is raining
• heavy rain is falling
• rain is coming down

So although the Latin is literal, it is perfectly normal Latin usage.

Dicit is present tense, third person singular, from dicere.

• mater dicit = mother says / the mother says

The present tense makes the statement immediate and current: she is saying this now.

The infinitives themselves are present infinitives, and in indirect statement they usually show action happening at the same time as the main verb.

So if mater dicit is present, then:

• pueros manere debere means that the boys ought to stay / that the boys should stay

It is not mainly about past or future time; it is about what is true or required at the time of her speaking.

Because quia introduces a reason or explanation, and here that reason is presented as a fact:

• quia pluvia gravis cadit = because heavy rain is falling

Latin normally uses the indicative after quia when the reason is treated as real or factual.

It can cover a range of meanings depending on context.

Debere can mean:

• ought to
• should
• must
• have to

In this sentence, the tone is probably practical rather than absolute, so English might translate it as:

• should stay inside
• ought to stay inside
• have to stay inside

All are possible, but ought to or should often fits well in a teaching example like this.

Latin word order is much more flexible than English word order because Latin uses case endings to show grammatical relationships.

Here:

• Mater = subject
• dicit = main verb
• pueros = accusative subject of the indirect statement
• intra domum = prepositional phrase
• manere debere = infinitives
• quia pluvia gravis cadit = reason clause

English relies heavily on word order, but Latin can move words around for emphasis, rhythm, or style. Even so, this sentence is fairly straightforward and natural.

Yes. Pueri often means boys, but in some contexts it can be understood more broadly as children, especially if the exact age or gender is not the main point.

In many beginner sentences, though, pueri/pueros is best understood simply as boys unless the context suggests otherwise.

Latin has no articles like English the or a/an.

So mater can mean:

• mother
• a mother
• the mother

The context tells you which is most natural. Here, English would probably translate it as Mother or The mother, depending on the style of translation.