Из кармана куртки выпал ключ.

Из means out of / from inside. It is used when something moves from the inside of something else to the outside.

So:

• из кармана = out of the pocket
• not с кармана, because с is more for movement off a surface
• not в кармане, because в would mean in the pocket, not movement out of it

The sentence describes the key leaving the pocket, so из is the natural preposition.

Because из requires the genitive case.

The dictionary form is:

• карман = pocket

After из, it becomes:

• из кармана = out of the pocket

So кармана is the genitive singular form of карман.

Because куртки depends on кармана and means of the jacket.

Russian often uses this pattern:

• X Y-а / Y-и = the X of the Y

So:

• карман куртки = the pocket of the jacket
• из кармана куртки = out of the pocket of the jacket

In natural English, we would usually say out of the jacket pocket.

It is best parsed like this:

• из [кармана куртки]
• out of [the pocket of the jacket]

So куртки goes with кармана, not with the whole sentence in some separate way.

A native English speaker may want to translate it literally, but the most natural English version is:

• out of the jacket pocket

Выпал comes from the verb выпасть, which means to fall out.

So this is not just fell in a general sense. It specifically means that the key was inside the pocket and then came out by falling.

That is why выпал is a very good choice here:

• ключ выпал = the key fell out

This is a very common question.

• выпал = fell out (from inside something)
• упал = fell down / fell in a general sense

Compare:

• Из кармана выпал ключ. = A/The key fell out of the pocket.
• Ключ упал на пол. = The key fell onto the floor.

In this sentence, the important idea is that the key came out of the pocket, so выпал is better than упал.

Because Russian past-tense verbs agree in gender and number with the subject.

The subject here is:

• ключ = key

And ключ is:

• masculine
• singular

So the verb is:

• выпал = masculine singular past

Compare:

• ключ выпал = the key fell out
• монета выпала = the coin fell out
• ключи выпали = the keys fell out

Russian word order is flexible, and the end of the sentence often carries the new or important information.

So:

• Из кармана куртки выпал ключ.

can feel like:

• Out of the jacket pocket fell a key.

The sentence first sets the scene (from the jacket pocket), then gives the event, then names what it was (a key).

You could also say:

• Ключ выпал из кармана куртки.

That is also correct, but it puts ключ earlier and sounds more like you are talking about the key as the topic.

Because ключ is the subject of the sentence — the thing that fell out.

In Russian, the subject is normally in the nominative case.

So here:

• ключ = nominative singular
• it is the thing performing the action of выпал

Even though it comes after the verb, it is still the subject.

It can mean either, depending on context.

Russian has no articles, so ключ by itself does not show the difference between a key and the key.

So this sentence could mean:

• A key fell out of the jacket pocket.
• The key fell out of the jacket pocket.

You understand which one is meant from the situation, not from an article.

Yes, absolutely.

Both are correct:

• Из кармана куртки выпал ключ.
• Ключ выпал из кармана куртки.

The difference is mainly emphasis and information flow.

• Из кармана куртки выпал ключ.
  Focuses first on where from, then reveals what fell out.

• Ключ выпал из кармана куртки.
  Starts with the key as the topic.

So the original sentence is not strange — it is just using normal Russian word order for a particular emphasis.