Addig a peronon várunk, amíg a járat megérkezik.

It is a very common Hungarian pair meaning until or more literally up to the point when.

So:

Addig ... amíg ... = until ...

In this sentence, Addig a peronon várunk, amíg a járat megérkezik means that we keep waiting on the platform up to the moment when the service arrives.

A very literal breakdown is:

• addig = until then / up to that point
• amíg = until / while / as long as
• together: until

Amíg alone can often be enough, but addig ... amíg is a very natural matched pair in Hungarian.

So all of these are possible:

• A peronon várunk, amíg a járat megérkezik.
• Addig várunk a peronon, amíg a járat megérkezik.
• Addig a peronon várunk, amíg a járat megérkezik.

Using both addig and amíg makes the time relationship very clear and often sounds nicely balanced.

Yes. Amíg can mean while, as long as, or until, depending on context.

For example:

• Amíg főzök, zenét hallgatok. = While I cook, I listen to music.
• Várj itt, amíg visszajövök. = Wait here until I come back.

In your sentence, because of addig ... amíg and the overall meaning, until is the natural interpretation.

The ending -on is a location ending, part of the set -on/-en/-ön, and here it means on or at the platform.

So:

• peron = platform
• peronon = on the platform

Hungarian often uses this ending where English uses on or sometimes at.

Because peronon shows location, while peronra shows movement toward the platform.

Compare:

• a peronon várunk = we are waiting on the platform
• a peronra megyünk = we are going onto/to the platform

So in your sentence, the people are already there, waiting, so the location form peronon is correct.

Várunk comes from the verb vár, meaning to wait.

The ending -unk means we in the present tense, so:

• várok = I wait
• vársz = you wait
• vár = he/she/it waits
• várunk = we wait

In English, you might translate it as we wait or we are waiting, depending on context. Hungarian present tense can cover both of those English possibilities.

Because Hungarian does not use várni the same way English uses wait for.

In English:

• wait for the train

In Hungarian, you usually either:

• use vár with a direct object, or
• just use vár by itself if the context already makes it clear

For example:

• A járatot várjuk. = We are waiting for the service.
• Várunk, amíg megérkezik. = We wait until it arrives.

So Hungarian does not need a separate word corresponding to English for here.

Járat usually means a service, route, run, or scheduled departure/arrival.

It is more general than vonat, which specifically means train.

So járat could refer to:

• a train service
• a bus service
• a flight
• another scheduled transport service

Because the sentence also mentions peron meaning platform, the most natural interpretation is probably a train or similar transport service, but járat itself is broader than train.

Because a is the definite article, meaning the.

So:

• a járat = the service
• a peronon = on the platform

Hungarian uses definite articles a lot, much like English. Here it suggests that the speaker has a specific platform and a specific service in mind, not just any random one.

Megérkezik means arrives.

It is built from:

• érkezik = arrives / is arriving
• megérkezik = arrives, with the sense of reaching the endpoint

In many cases, meg- adds a sense of completion or attainment of a result. With érkezik, the form megérkezik is very common and often the most natural way to say arrive.

So in this sentence, a járat megérkezik means the service arrives.

Because Hungarian often uses the present tense for future events, especially in time clauses like this one.

So Hungarian commonly says things like:

• Amikor megjön, elindulunk. = When he comes, we will leave.
• Várunk, amíg megérkezik. = We wait until it arrives.

English often uses present tense in these subordinate time clauses too, so this is actually fairly similar:

• not usually until it will arrive
• but until it arrives

So megérkezik is perfectly normal here.

Yes. Hungarian word order is flexible, and changing it often changes emphasis rather than basic meaning.

For example, you could also say:

• A peronon várunk addig, amíg a járat megérkezik.
• Addig várunk a peronon, amíg a járat megérkezik.

The version you have:

Addig a peronon várunk, amíg a járat megérkezik.

puts addig early, which highlights the duration: we wait until that point. It sounds natural and clear.

Yes, it is grammatical and natural.

That said, in everyday speech, some speakers might choose a slightly simpler version such as:

• A peronon várunk, amíg a járat megérkezik.

But your original sentence is completely fine and sounds like normal Hungarian.