Meni se sviđaju sveže jabuke.

Because the verb sviđati se works differently from English to like.

In Serbian, the person who feels the liking is put in the dative case, not the nominative. So:

• ja = I
• meni = to me

A very literal way to understand the sentence is:

Fresh apples are pleasing to me.

So meni is correct because it means to me, which is the structure this verb requires.

In this sentence, se is part of the verb expression sviđati se. You should learn it as a whole verb:

• sviđati se = to be pleasing / to appeal / to be liked

Here, se does not mean self in the English sense. It is just a fixed part of the verb.

So it is not something optional in this expression. You normally say:

• sviđa mi se
• sviđaju mi se

not just sviđa mi or sviđaju mi.

Because the verb agrees with jabuke, which is plural.

The thing being liked is the grammatical subject in Serbian with sviđati se, so the verb must match it:

• jabuka = apple → singular → sviđa se
• jabuke = apples → plural → sviđaju se

So:

• Meni se sviđa sveža jabuka. = I like a fresh apple.
• Meni se sviđaju sveže jabuke. = I like fresh apples.

Here jabuke is nominative plural.

That may feel surprising to an English speaker, because in English apples feels like the object of like. But with sviđati se, the thing liked is actually the subject of the sentence.

So in this sentence:

• meni = dative experiencer
• jabuke = nominative plural subject

A useful literal model is:

Fresh apples please me.

Also, the form jabuke can look the same as accusative plural, but here it is functioning as nominative, and you can tell partly because the verb agrees with it in the plural.

Because adjectives in Serbian must agree with the noun they describe in gender, number, and case.

Here the noun is:

• jabuke = feminine plural nominative

So the adjective must also be feminine plural nominative:

• sveže jabuke = fresh apples

Compare:

• sveža jabuka = fresh apple
• sveže jabuke = fresh apples

So the ending changes because the noun changes.

Yes, absolutely. That is a very natural word order.

In fact, Sviđaju mi se sveže jabuke may sound more neutral in everyday Serbian. Serbian word order is flexible, and different orders can change emphasis.

Compare:

• Sviđaju mi se sveže jabuke. = neutral, natural
• Meni se sviđaju sveže jabuke. = puts more emphasis on meni, like I like fresh apples / As for me, I like fresh apples

So both are correct, but the version with meni at the start often sounds more emphatic or contrastive.

Both are dative forms meaning to me, but they are used differently:

• mi = unstressed clitic form
• meni = full, stressed form

The shorter mi is very common in ordinary sentences:

• Sviđaju mi se sveže jabuke.

The full form meni is used when you want emphasis, contrast, or extra clarity:

• Meni se sviđaju sveže jabuke, ali njemu ne.
  I like fresh apples, but he doesn’t.

So in your sentence, meni adds emphasis.

The dictionary form is sviđati se.

In your sentence, sviđaju is the 3rd person plural present tense form, used because jabuke is plural.

A simplified pattern is:

• sviđa se = singular
• sviđaju se = plural

Examples:

• Sviđa mi se knjiga. = I like the book.
• Sviđaju mi se knjige. = I like the books.

So when you see sviđaju, think of it as the plural present form of sviđati se.

You would say:

Meni se sviđa sveža jabuka.

The changes are:

• jabuke → jabuka because it is now singular
• sviđaju → sviđa because the subject is now singular
• sveže → sveža because the adjective must agree with the singular noun

So:

• Meni se sviđa sveža jabuka. = I like a fresh apple.
• Meni se sviđaju sveže jabuke. = I like fresh apples.

Usually it can mean either, depending on context.

Without more context, Meni se sviđaju sveže jabuke is most naturally understood as a general preference:

I like fresh apples.

But in the right situation, it could also mean that the speaker likes some fresh apples being discussed or seen at that moment.

Serbian often relies on context more than English for this kind of distinction. The sentence itself does not force only one interpretation.