A katonai épület nagy.

In Hungarian, the verb to be is usually left out in the present tense when the subject is third person singular or plural.

So:

• A katonai épület nagy. = The military building is big.

But in other persons, the verb appears:

• Én nagy vagyok. = I am big.
• Te nagy vagy. = You are big.

So the missing is is completely normal here.

A is the definite article, meaning the.

• a is used before most consonant sounds
• az is used before vowel sounds

So:

• a katonai épület = the military building
• az épület = the building

Hungarian does not use a/an the same way English does. Here, a specifically means the.

Because in Hungarian, attributive adjectives normally come before the noun, just like in English.

So:

• katonai épület = military building
• nagy épület = big building

This is the normal order:

• adjective + noun

No. Hungarian adjectives usually do not agree with the noun in gender, number, or case when they come before it.

So:

• katonai épület = military building
• katonai épületek = military buildings

Notice that katonai stays the same. Only the noun changes.

This is much simpler than in many Indo-European languages.

Here nagy is the predicate adjective, meaning it describes the subject through an implied is.

Structure:

• A katonai épület = the subject
• nagy = the description

So the sentence is literally structured like:

• The military building — big.

This is a very normal Hungarian sentence pattern.

Hungarian word order is fairly flexible, but the neutral order here is completely natural.

Yes. Nagy a katonai épület is also correct.

The difference is mainly focus/emphasis:

• A katonai épület nagy. = neutral statement
• Nagy a katonai épület. = emphasis on big

The second version can sound like:

• The military building is big
• or even The military building is big, actually

So both are grammatical, but the word order changes the emphasis.

Yes. Katonai is related to katona, which means soldier.

The suffix -i often makes an adjective meaning related to, belonging to, or connected with something.

So:

• katona = soldier
• katonai = military / army-related

Other examples of -i:

• iskola = school → iskolai = school-related
• Budapest → budapesti = from Budapest / Budapest-related
  (this one uses a slightly different form)

So katonai épület means a building connected with the military.

Because it is the subject of the sentence, and Hungarian subjects are normally in the basic dictionary form, called the nominative.

So:

• épület = building
• a katonai épület = the military building

No extra ending is needed because the noun is simply the subject.

Hungarian adds endings when a noun has another role, for example:

• épületben = in the building
• épületet = building (object)
• épülethez = to the building

But here, plain épület is correct.

The Hungarian gy is a special sound that does not exist exactly in standard English.

A useful approximation is something like:

• a soft dy sound

So nagy sounds roughly like nody or nady, but not exactly.

A more precise pronunciation is:

• nagy ≈ /nɒɟ/

Also, Hungarian stress is almost always on the first syllable, so:

• NAgy
• KAtonai
• ÉPület

That first-syllable stress is very important in Hungarian pronunciation.

Yes. Nagy most commonly means big or large, but depending on context it can also mean things like:

• great
• important
• grown-up
• older

For example:

• nagy ház = big house
• nagy ember = important/great man
• nagy fiú = big boy / older boy

In A katonai épület nagy, the meaning is clearly the physical one: big/large.

It is neutral and completely normal Hungarian.

Nothing in it is especially formal or especially casual. It is the kind of simple descriptive sentence you would often see in a textbook because it shows several basic patterns clearly:

• definite article: a
• adjective before noun: katonai épület
• omitted is in present tense: nagy

So it is a very standard model sentence.