A borítékon rajta van a cím, de a levelet még nem adtam fel.

Because Hungarian only drops the 3rd-person present copula in some kinds of sentences.

• With a noun or adjective predicate, van is usually omitted:
  • Ő tanár. = He/She is a teacher.
  • A ház nagy. = The house is big.
• But with location or existence, van is normally kept:
  • A könyv az asztalon van. = The book is on the table.

Here, rajta van a cím means the address is on it / on there, so this is a location-type sentence, and van is needed.

Rajta means on it.

It is the 3rd-person form in the series:

• rajtam = on me
• rajtad = on you
• rajta = on him/her/it

So:

• A borítékon = on the envelope
• rajta van a cím = the address is on it

Hungarian often uses this kind of resumptive word to point back to something already mentioned. It can make the sentence sound more natural and can emphasize that something is physically present on the surface.

So the sentence feels a bit like:

• As for the envelope, the address is on it...

A shorter version without rajta can exist in some contexts, but rajta van is very natural here.

Because -on / -en / -ön is the suffix meaning on for many nouns.

• boríték = envelope
• borítékon = on the envelope

This is called the superessive case.

The exact form of the suffix depends on vowel harmony and the shape of the word. Since boríték contains a back vowel (o), it takes the -on form.

Because levelet is the accusative form, which marks the direct object.

• levél = letter
• levelet = letter (as the thing being acted on)

In this sentence, the letter is what the speaker has not posted, so it needs the object ending -t.

Also note that some Hungarian nouns do not simply add -t directly; they may insert a linking vowel or change shape slightly. So:

• levél → levelet not just levélt

Because in Hungarian, when a verb with a preverb is negated, the preverb usually moves after the verb.

The basic verb here is:

• felad = to post / mail

In a normal affirmative sentence:

• Feladtam a levelet. = I posted the letter.

But with negation:

• Nem adtam fel a levelet. = I did not post the letter.

So in your sentence:

• a levelet még nem adtam fel

this is exactly the expected pattern.

Még nem means not yet.

• még can mean still / yet
• nem = not

Together:

• még nem adtam fel = I haven’t posted it yet

A useful contrast is:

• még nem = not yet
• már nem = no longer / not anymore

So:

• Még nem jött meg. = It hasn’t arrived yet.
• Már nem itt lakik. = He/She no longer lives here.

Here, felad means to post / mail / send off a letter or package.

With different objects, felad can have different meanings. Hungarian preverbs often create meanings that are not fully predictable from the base verb alone.

Examples:

• feladni a levelet = to mail the letter
• feladni a csomagot = to send/post the package
• feladni can also mean to give up in other contexts

So you should learn feladni a levelet as a natural expression meaning to post a letter.

Hungarian word order is much more about topic and emphasis than fixed English-style subject-verb-object order.

In this sentence:

• A borítékon sets the scene: as for the envelope / on the envelope
• rajta van a cím gives the information about it
• de introduces contrast: but
• a levelet is the thing being contrasted
• még nem adtam fel gives the key new information: I haven’t posted it yet

So the sentence is not just mechanically ordered; it is structured around what is already being talked about and what is being contrasted.

A rough feel in English might be:

• The address is on the envelope, but the letter I haven’t posted yet.

That sounds marked in English, but in Hungarian this kind of information-based ordering is very normal.

A is the definite article, like English the.

So:

• a borítékon = on the envelope
• a cím = the address
• a levelet = the letter

Hungarian uses the definite article with specific, identifiable things, much like English. In this sentence, the speaker is talking about a particular envelope, a particular address, and a particular letter.

No. Cím can mean both:

• address
• title

Context tells you which one is meant.

Examples:

• Mi a címed? = What is your address?
• Mi a könyv címe? = What is the title of the book?

In A borítékon rajta van a cím, it clearly means address, because it is talking about something written on an envelope.

Yes. Hungarian often allows several word orders, but the emphasis changes.

For example, you may also hear things like:

• A cím rajta van a borítékon, de a levelet még nem adtam fel.
• A borítékon van a cím, de a levelet még nem adtam fel.

These are all close in meaning, but they do not highlight exactly the same thing.

Your original version is natural because it first sets up the envelope, then says the address is on it, and then contrasts that with but I still haven’t posted the letter.