A próbalencse az asztalon van.

Hungarian has one definite article, but it has two forms:

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

So here:

• a próbalencse = the trial lens because próbalencse starts with a consonant
• az asztalon = on the table / literally on the table because asztalon starts with a vowel

This is similar to how English has a and an, but in Hungarian this alternation happens with the, not the indefinite article.

Asztal means table.

The ending -on is a case ending meaning on for many nouns. So:

• asztal = table
• asztalon = on the table

This is one of the Hungarian location endings. Instead of using a separate preposition like English on, Hungarian often puts the location meaning directly on the noun.

Hungarian usually expresses many meanings like in, on, at, to, from, etc. with suffixes attached to nouns rather than separate prepositions.

So English says:

• on the table

Hungarian says:

• az asztalon

where -on carries the meaning on.

This is a very common feature of Hungarian grammar.

That is a very common and important question.

Hungarian often omits van (is) in the present tense, third person, when the predicate is a noun or adjective:

• Ő orvos. = He/She is a doctor.
• A ház nagy. = The house is big.

But when you are talking about location or existence, van is normally used:

• A könyv az asztalon van. = The book is on the table.
• A próbalencse az asztalon van. = The trial lens is on the table.

So in this sentence, van is necessary because the sentence tells us where something is.

That is the normal neutral position here.

Hungarian word order is flexible, but it is strongly connected to focus and emphasis. In a neutral sentence about location, a common order is:

• [Subject] + [place expression] + van

So:

• A próbalencse az asztalon van.

This sounds like a neutral statement: The trial lens is on the table.

Other word orders are possible, but they usually change the emphasis.

Yes. That is also grammatical.

• A próbalencse az asztalon van. = neutral, topic-first, the trial lens is what we are talking about
• Az asztalon van a próbalencse. = more like The trial lens is on the table with stronger attention on the location, or as an answer to Where is the trial lens?

Both are correct, but they are used in slightly different discourse situations.

Because Hungarian usually writes compounds as one word.

• próba = test / trial
• lencse = lens

Together:

• próbalencse = trial lens / test lens

This is very normal in Hungarian. English often uses two words where Hungarian prefers one compound word.

A helpful rough pronunciation is:

• pró-ba-len-che

A few notes:

• ó is a long o
• e is like a short e
• cs in Hungarian is pronounced like English ch in chair

So lencse sounds roughly like LEN-che.

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

• PRÓ-balencse
• ASZ-talon

It is a location phrase meaning on the table.

More literally:

• az = the
• asztalon = on table / on the table

Together, it tells us where the subject is.

So the sentence structure is:

• A próbalencse = the subject
• az asztalon = the location
• van = is

Hungarian does not have grammatical gender. There is no masculine/feminine distinction like he/she built into nouns.

Also, Hungarian often does not need a subject pronoun when the subject is already stated or understood. Here the noun itself is the subject:

• A próbalencse = the trial lens

So there is no need to add a separate word like it.

In this sentence, az asztalon means on the table, so the table is definite.

You could make it indefinite if the meaning required it:

• egy asztalon = on a table

So:

• A próbalencse egy asztalon van. = The trial lens is on a table.

That is possible, but it means something slightly different. Your original sentence refers to a specific table.

It is in the superessive case.

The superessive usually expresses the idea of being on the surface of something.

For example:

• asztalon = on the table
• földön = on the ground
• széken = on the chair

The common endings are:

• -on
• -en
• -ön

The exact form depends on the word.

Hungarian case endings often change form depending on vowel harmony and the shape of the word.

For the superessive case, the ending can appear as:

• -on
• -en
• -ön

With asztal, the correct form is:

• asztalon

Unfortunately, with some noun endings you simply have to learn which variant is used, although vowel harmony gives you a strong clue. Over time these forms become familiar through exposure.

Yes. It is a very normal sentence pattern for stating location:

• [definite noun] + [place expression] + van

For example:

• A könyv az asztalon van. = The book is on the table.
• A kulcs a táskában van. = The key is in the bag.
• A próbalencse az asztalon van. = The trial lens is on the table.

So this sentence is a good model for many similar sentences.