Ez a csomagszám.

In Hungarian, the verb van (to be) is often omitted in the present tense, third person when the sentence links one thing to another noun or adjective.

So:

Ez a csomagszám.
literally looks like This the package number,
but it means This is the package number.

This is completely normal Hungarian.

The verb appears again in other tenses or persons, for example:

• Ez volt a csomagszám. = This was the package number.
• Én vagyok a sofőr. = I am the driver.

Because Hungarian normally uses the pattern:

ez a + noun = this + noun
az a + noun = that + noun

So:

• ez a csomagszám = this package number / this is the package number (depending on context)

You generally cannot just say ez csomagszám. The article is part of the normal structure when ez directly modifies a noun.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Since csomagszám starts with cs, which is a consonant sound, the correct form is:

a csomagszám

Compare:

• a ház = the house
• az ablak = the window

It is a compound noun made from:

• csomag = package / parcel
• szám = number

So csomagszám literally means package-number.

Hungarian very often forms compounds this way, and they are usually written as one word.

Yes. Hungarian usually writes this kind of compound as a single word.

So:

• csomagszám = one word

This is very common in Hungarian, where English might use two words or a noun + noun structure.

Other similar examples are:

• telefonszám = telephone number
• házszám = house number

A rough English-friendly pronunciation is:

ez aw CHO-mag-saam

Useful spelling points:

• cs is pronounced like English ch
• sz is pronounced like English s
• á is a long a sound
• stress in Hungarian usually falls on the first syllable of the word

So csomagszám sounds roughly like:

CHO-mag-saam

Ez a csomagszám. is the most neutral and natural order.

Hungarian word order is flexible, but changing it usually changes the emphasis or makes the sentence sound marked.

So a learner should treat:

Ez a csomagszám.

as the standard version.

A different order may be possible in special contexts, but it is not the basic pattern you should learn first.

You would use egy for a/an:

Ez egy csomagszám.

Compare:

• Ez a csomagszám. = This is the package number.
• Ez egy csomagszám. = This is a package number.

So a here is the definite article (the), while egy is the indefinite article (a/an).

It can definitely be used by itself.

For example:

• Mi ez? = What is this?
• Ez jó. = This is good.

But when ez directly goes with a noun, Hungarian normally uses:

ez a + noun

So:

• ez = this
• ez a csomagszám = this package number / this is the package number

That is why the article appears in your sentence.