Pater dicit se diem festum cum familia celebraturum esse.

Because this is an indirect statement after dicit (he says), and Latin normally uses the accusative + infinitive construction for that.

So instead of saying something like that he will celebrate... with a separate that-clause, Latin says:

• se = himself / he as the subject of the reported statement, in the accusative
• celebraturum esse = to be going to celebrate / will celebrate

Se is specifically the reflexive pronoun, referring back to the subject of the main verb, here pater. So:

• Pater dicit se... = The father says that he...
• and se refers back to pater

If Latin used eum instead, that would normally mean that some other male person would celebrate, not the father himself.

It is an indirect statement (also called accusative and infinitive, often abbreviated AcI).

After verbs of saying, thinking, knowing, hearing, and perceiving, Latin often uses:

• a subject in the accusative
• plus an infinitive

Here:

• se = accusative subject of the indirect statement
• celebraturum esse = future infinitive

So literally the structure is:

• Pater dicit = Father says
• se... celebraturum esse = that he will celebrate...

English uses that plus a finite verb; Latin usually does not.

Because celebraturum esse is the future active infinitive of celebrare.

It is formed from:

• the future active participle: celebraturus
• plus esse

So:

• celebraturus esse = to be going to celebrate
• in indirect statement, this is usually best translated as will celebrate

Since the subject of the infinitive is se (accusative, masculine singular), the participle appears as:

• celebraturum
  because it agrees with se in gender, number, and case

So the whole phrase means:

• that he will celebrate

Because celebraturum must agree with se, and se is accusative.

The future active participle behaves like an adjective, so it changes form to match the noun or pronoun it goes with.

Here the understood full agreement is:

• se = masculine singular accusative
• therefore celebraturum

Compare:

• nominative masculine singular: celebraturus
• accusative masculine singular: celebraturum

Since the subject of the indirect statement is in the accusative, the participle must be accusative too.

Because it is the direct object of celebrare.

The verb celebrare takes an object: you celebrate something.
So:

• diem festum = a holiday / festival day

It is accusative because it is the thing being celebrated.

The sentence structure is:

• se = subject of the infinitive
• diem festum = object of the infinitive
• cum familia = prepositional phrase
• celebraturum esse = future infinitive

Literally it means a festival day or a feast day.

Depending on context, it can be translated more naturally as:

• a holiday
• a festival
• a feast day
• a special day of celebration

So in this sentence, it most naturally means something like a holiday or a festival day.

Because cum means with, and it takes the ablative case.

So:

• familia here is ablative singular
• cum familia = with the family or with his family

Latin often uses cum + ablative to express accompaniment.

Examples:

• cum amico = with a friend
• cum sorore = with his/her sister
• cum familia = with the family

Yes, very often Latin leaves that kind of possession unstated when it is obvious from context.

Since se refers back to pater, the natural understanding is:

• cum familia = with his family

Latin does not always need to add sua unless emphasis or clarity is needed.

So:

• cum familia can naturally mean with the family
• in context, English will often translate it as with his family

Because Latin normally does not introduce indirect statements with a conjunction equivalent to English that.

English says:

• Father says that he will celebrate...

Latin instead says:

• Father says himself to-be-going-to-celebrate...

That sounds strange in English, but it is the normal Latin pattern. The idea of that is built into the accusative + infinitive construction.

So there is no missing word here; the sentence is grammatically complete as it stands.

Because se is a reflexive pronoun, and in this kind of sentence it normally points back to the subject of the main clause.

Main clause:

• Pater dicit = Father says

Indirect statement:

• se... celebraturum esse = that he will celebrate...

So the default reading is:

• The father says that he himself will celebrate...

If Latin wanted to say the father says that another man will celebrate, it would usually use a different pronoun, such as eum.

The word order is flexible, but the chosen order is natural and clear.

Latin uses endings more than position to show function, so the parts can often move around without changing the basic meaning.

Here:

• Pater = subject of dicit
• dicit = main verb
• se = subject of the indirect statement
• diem festum = object
• cum familia = prepositional phrase
• celebraturum esse = future infinitive

Placing celebraturum esse at the end is very normal, since Latin often puts the verb or verbal phrase near the end of the clause.

Only awkwardly. A very literal rendering would be something like:

• Father says himself a festival day with family about-to-celebrate to be.

That is not good English, but it shows the Latin structure.

A normal English translation is:

• Father says that he will celebrate the holiday with his family.

So it is better to understand the grammar rather than try to translate each word mechanically.

It comes from the verb celebro, celebrare, celebravi, celebratum = to celebrate.

The form celebraturum is not something you would list in a dictionary by itself. It is the accusative masculine singular of the future active participle:

• nominative: celebraturus
• accusative: celebraturum

Then with esse, it forms the future infinitive:

• celebraturum esse = to be going to celebrate / to celebrate in the future