Objasni mi čemu služi ovaj mali gumb na otvaraču.

Objasni is the imperative form of the verb objasniti (to explain).

So Objasni mi ... means Explain to me ...

A few useful points:

• objasniti = perfective verb, often used for a single completed explanation
• objasni = imperative, you singular
• Croatian often leaves out the subject pronoun ti (you) because it is already clear from the verb form

So:

• Objasni mi ... = Explain to me ...
• Objasnite mi ... = Explain to me ... (plural or polite)

Mi here means to me.

It is the dative clitic form of ja (I):

• ja = I
• meni = to me
• mi = to me (short/clitic form)

So:

• Objasni mi = Explain to me

The short form mi is very common in everyday Croatian.

Compare:

• Objasni mi. = Explain to me.
• Objasni meni. = Explain to me. (more emphasis)

Because the verb služiti in this meaning often goes with the dative case.

So čemu is the dative form of što/what:

• što = what
• čemu = to what / what for

In this sentence, čemu služi means something like:

• what is it for?
• what does it serve for?
• what is it used for?

This is a very common Croatian pattern:

• Čemu to služi? = What is that for?
• Čemu služi ovaj gumb? = What is this button for?

So even though English uses what for, Croatian uses a dative form: čemu.

Služi is the 3rd person singular present tense of služiti.

Here it means:

• serves
• is used
• is for

So:

• čemu služi ovaj mali gumb
  literally: what does this small button serve for more naturally: what is this small button for

Useful examples:

• Ovo služi za rezanje. = This is used for cutting.
• Čemu služi ovaj alat? = What is this tool for?

Yes, za što služi is also possible, but čemu služi is very common and often feels very natural.

Compare:

• Čemu služi ovaj gumb?
• Za što služi ovaj gumb?

Both mean roughly:

• What is this button for?

A related structure is:

• Ovaj gumb služi za otvaranje. = This button is used for opening.

So Croatian can express this idea in more than one way:

1. čemu služi = what is it for
2. za što služi = what is it for
3. služi za + accusative / verbal noun = is used for ...

Ovaj mali gumb is in the nominative singular.

Why? Because it is the subject of služi.

Breakdown:

• ovaj = this
• mali = small
• gumb = button

All three agree in:

• gender: masculine
• number: singular
• case: nominative

So the phrase means:

• this small button

Otvaraču is in the locative singular.

That is because na can take different cases depending on meaning:

• na + locative = location (on, at)
• na + accusative = movement toward a surface/place

Here the meaning is location:

• gumb na otvaraču = the button on the opener

So:

• na otvaraču = on the opener

Compare:

• Gumb je na otvaraču. = The button is on the opener.
• Stavi gumb na otvarač. = Put the button onto the opener.

In the second example, there is movement, so the case changes.

The dictionary form is otvarač.

It is a masculine noun, and here it changes because of case:

• otvarač = nominative singular
• otvaraču = locative singular

So:

• otvarač = opener
• na otvaraču = on the opener

This kind of ending change is very normal in Croatian. Nouns change form depending on their role in the sentence.

Croatian word order is more flexible than English word order, but there are still patterns.

In this sentence:

• Objasni = main command
• mi = short unstressed pronoun, which usually comes very early, often in the second position
• čemu služi ovaj mali gumb na otvaraču = the clause being explained

So Objasni mi ... is a very natural order.

You may also hear variations, depending on emphasis, for example:

• Objasni mi čemu služi ovaj mali gumb na otvaraču.
• Čemu služi ovaj mali gumb na otvaraču, objasni mi.
  (less neutral, more marked)

For learners, the main thing to remember is: short forms like mi usually appear near the beginning, not later in the sentence.

Both can mean to me, but they are used differently.

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

In a neutral sentence, Croatian usually prefers the short form:

• Objasni mi ... = neutral, natural

Use meni for emphasis or contrast:

• Objasni meni, ne njemu. = Explain to me, not to him.

So in your sentence, mi is the normal choice.

Croatian does not have articles like English a and the.

Instead, Croatian shows definiteness in other ways, often through:

• context
• word order
• demonstratives such as ovaj (this), taj (that)

So:

• gumb = a button / the button (depending on context)
• ovaj gumb = this button

In your sentence, ovaj already makes the noun specific, so English would naturally say this small button.

Both gumb and otvarač are masculine singular nouns.

You can see this from the agreement:

• ovaj = masculine singular demonstrative
• mali = masculine singular adjective

So:

• ovaj mali gumb must be masculine singular

Also:

• otvarač is masculine
• na otvaraču shows the locative singular form of a masculine noun

This matters because adjectives, pronouns, and some verb forms must agree with the noun.

Yes. The given sentence uses the singular informal imperative Objasni.

To make it polite or address more than one person, use:

• Objasnite mi čemu služi ovaj mali gumb na otvaraču.

So:

• Objasni mi ... = explain to me ... (to one person, informal)
• Objasnite mi ... = explain to me ... (polite or plural)

This is one of the most useful verb-form distinctions in Croatian.

A few natural alternatives are:

• Čemu služi ovaj mali gumb na otvaraču?
  = What is this small button on the opener for?

• Možeš mi objasniti čemu služi ovaj mali gumb na otvaraču?
  = Can you explain to me what this small button on the opener is for?

• Za što služi ovaj mali gumb na otvaraču?
  = What is this small button on the opener for?

Your original sentence is perfectly natural; these are just common variations.