Magistra dicit historiam regni antiqui discipulis utilem esse.

Because after dicit Latin is using an indirect statement construction.

In English, we say:

• The teacher says that the history ... is useful.

Latin usually does not use a separate word for that here. Instead, it uses:

• a verb of saying/thinking/perceiving
• plus an accusative subject
• plus an infinitive

So in:

• Magistra dicit historiam ... utilem esse

the word historiam is the subject of the infinitive esse, but in an indirect statement that subject goes into the accusative.

So historiam is accusative not because it is the direct object of esse—infinitives do not take objects that way—but because it is the subject of the embedded statement.

It is the standard Latin accusative-and-infinitive construction, often abbreviated ACI.

Here is the pattern:

• dicit = she says
• historiam ... utilem esse = the history to be useful

Put naturally into English, that becomes:

• she says that the history is useful

So Latin expresses that X is Y after a verb like dicit by putting:

• X in the accusative
• Y agreeing with it
• esse for to be

That is why the clause looks different from English.

Because utilem goes with historiam.

In the indirect statement:

• historiam = the history/story
• utilem = useful

Since historiam is feminine singular accusative, the adjective describing it must match:

• feminine
• singular
• accusative

So:

• historia utilis est = the history is useful
• but after dicit this becomes
• historiam utilem esse = that the history is useful

The adjective changes case along with the noun it describes.

The endings tell you.

• historiam is feminine singular accusative
• utilem is feminine singular accusative

So those two match.

But:

• discipulis is dative plural
• utilem is not dative plural, so it cannot describe discipulis

Instead, discipulis depends on utilem in sense: the history is useful to the students.

So the structure is:

• historiam = subject of the infinitive
• utilem = predicate adjective with historiam
• discipulis = dative with useful

Because utilis often takes the dative of the person or thing for whom something is useful.

So:

• utile discipulo = useful to the student
• utilis discipulis = useful to the students

In this sentence:

• discipulis = to the students / for the students

This is very common in Latin with adjectives expressing suitability, friendliness, helpfulness, nearness, and similar ideas.

Because they mean of the ancient kingdom.

The noun regnum means kingdom. Its genitive singular is regni, meaning of the kingdom.

Since antiqui describes regni, it also appears in the genitive singular:

• regni antiqui = of the ancient kingdom

So historiam regni antiqui means:

• the history/story of the ancient kingdom

This is the normal Latin way to express of ... relationships.

The key issue is case, not just word order.

To mean of the ancient kingdom, Latin needs the genitive singular:

• regni antiqui

You could also say:

• antiqui regni

That would mean the same thing. Latin word order is flexible.

But regnum antiquum would be accusative singular (or nominative, depending on context), meaning something like the ancient kingdom, not of the ancient kingdom.

So the important distinction is:

• regni antiqui = of the ancient kingdom
• regnum antiquum = the ancient kingdom

The subject of the main verb dicit is magistra.

• Magistra = the teacher (female teacher)
• dicit = says

So at the main-clause level:

• Magistra dicit = The teacher says

Inside the indirect statement, there is another logical subject:

• historiam = the thing that is useful

So there are really two layers:

1. Main clause: magistra dicit
2. Indirect statement: historiam ... utilem esse

Because in this kind of sentence Latin usually does not need one.

English says:

• The teacher says that the history is useful.

Latin normally says:

• Magistra dicit historiam utilem esse.

The combination of:

• accusative noun (historiam)
• plus infinitive (esse)

already signals that-clause meaning after dicit.

So the idea of that is built into the construction rather than expressed by a separate word.

In classical Latin, with an indirect statement, esse is normally understood as part of the full construction, and it is often expressed clearly:

• historiam discipulis utilem esse

This corresponds to that the history is useful to the students.

Sometimes forms of esse can be omitted in certain contexts, especially in poetry or very compressed prose, but for a learner the normal and expected form here is with esse included.

So in this sentence, esse completes the indirect statement.

It is an adjective.

The dictionary form is:

• utilis, utile = useful

Here it appears as utilem, the feminine singular accusative form, because it agrees with historiam.

It is specifically a predicate adjective in the indirect statement:

• historiam utilem esse = the history to be useful

So it is not an adverb and not a noun; it is an adjective describing historiam.

Yes. Latin word order is much more flexible than English word order because the endings do so much of the grammatical work.

For example, these would still mean essentially the same thing:

• Magistra dicit historiam regni antiqui discipulis utilem esse.
• Magistra historiam regni antiqui utilem discipulis esse dicit.
• Historiam regni antiqui discipulis utilem esse magistra dicit.

Different orders can shift emphasis, but the grammatical relationships remain clear because of the cases:

• historiam = accusative
• regni antiqui = genitive
• discipulis = dative
• utilem = agreeing with historiam

So you should pay attention to endings more than to English-style word order.

It can mean either, depending on context.

Latin historia can refer to:

• a history
• an account
• a story/narrative

In this sentence, the surrounding words regni antiqui make history of the ancient kingdom a very natural interpretation, but the exact English choice depends on context.

So if your translation gives history, that is very likely right here; if it gives story/account, that is also understandable depending on the setting.

Because classical Latin has no articles.

So:

• magistra can mean the teacher or a teacher
• historiam can mean the history or a history

English forces you to choose an article, but Latin often leaves that to context.

In this sentence, English usually says:

• The teacher says that the history of the ancient kingdom is useful to the students

But Latin itself does not explicitly mark the.