Ova odgovornost mi je nova.

Because odgovornost is a feminine singular noun, and the demonstrative this has to agree with it.

Croatian has different forms of this depending on gender:

• ovaj = masculine
• ova = feminine
• ovo = neuter

So:

• ova odgovornost = this responsibility

Since odgovornost is feminine, ova is the correct form.

It is in the nominative singular.

In this sentence, ova odgovornost is the subject of the sentence, so nominative is expected.

A useful thing to notice is that odgovornost is one of those feminine nouns that ends in a consonant, not in -a. That can look unusual to English speakers, because many feminine nouns in Croatian do end in -a, but not all of them do.

So here:

• ova odgovornost = subject, nominative singular

Because adjectives in Croatian must agree with the noun they describe in:

• gender
• number
• case

The noun odgovornost is:

• feminine
• singular
• nominative

So the adjective must match it:

• nova

Compare:

• novi posao = a new job
• nova odgovornost = a new responsibility
• novo pitanje = a new question

That is why nova is used here, not novi or novo.

Mi here means to me.

It is the dative singular form of ja when used as a short clitic pronoun.

So:

• ja = I
• mene / me = me
• meni / mi = to me

In this sentence, Croatian uses the dative because the idea is basically:

• This responsibility is new to me

So mi is not I and not direct-object me. It specifically means to me.

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

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

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

• Ova odgovornost mi je nova.

You would use meni for emphasis, contrast, or after a preposition:

• Meni je ova odgovornost nova. = This responsibility is new to me specifically, maybe not to someone else.
• Za mene = for me

So mi is the normal unmarked choice here.

Je is the 3rd person singular form of the verb biti = to be.

Here it means is:

• Ova odgovornost mi je nova.
• literally: This responsibility to me is new.

Croatian often uses short clitic forms of to be in ordinary sentences:

• sam = am
• si = are
• je = is
• smo = are
• ste = are
• su = are

So je is simply the verb is.

Because both mi and je are clitics, and Croatian has rules about where clitics go.

Very roughly:

• clitics usually appear in the second position of the clause
• when several clitics occur together, they tend to appear in a fixed order

In this sentence, mi je is the normal order.

So:

• Ova odgovornost mi je nova. = natural
• Ova odgovornost je mi nova. = incorrect

For learners, the safest thing is to memorize common clitic combinations such as:

• mi je
• ti je
• mu je
• joj je
• nam je

It is not the normal neutral way to say it.

Croatian strongly prefers the clitic placement:

• Ova odgovornost mi je nova.

Using meni at the end sounds marked and usually adds emphasis or contrast:

• Ova odgovornost je nova meni, ali ne i tebi.
• This responsibility is new to me, but not to you.

So for ordinary use, stick with:

• Ova odgovornost mi je nova.

In this sentence, it most naturally means new to me, so unfamiliar or something I have not had before.

That is because of mi:

• nova by itself can mean new
• mi je nova strongly suggests is new to me

So this sentence is not mainly saying the responsibility was recently created. It is saying that the speaker is not used to it yet.

No, not this exact sentence.

Ova odgovornost mi je nova means:

• This responsibility is new to me

If you want This is my new responsibility, Croatian would say something like:

• Ovo je moja nova odgovornost.

Notice the difference:

• moja nova odgovornost = my new responsibility
• mi je nova = is new to me

That is an important distinction.

Because Croatian often expresses meanings like to me, for me, from me, etc. through case forms, not always with a separate preposition.

Here, mi is dative, and the dative already carries the idea of to me.

So English says:

• new to me

Croatian says:

• mi je nova
• literally something like is new to me, with to me expressed by the dative pronoun

This is very common in Croatian grammar.

Not very naturally.

A word-for-word breakdown is:

• ova = this
• odgovornost = responsibility
• mi = to me
• je = is
• nova = new

So literally:

• This responsibility to me is new

But natural English would be:

• This responsibility is new to me

This is a good example of why Croatian and English often organize the same idea differently.

Yes, very common.

Croatian often uses the dative pronoun to show how something relates to a person:

• To mi je jasno. = That is clear to me.
• Ona mi je draga. = She is dear to me / I am fond of her.
• Ovo mi je teško. = This is hard for me.
• Ova odgovornost mi je nova. = This responsibility is new to me.

So this sentence follows a very common Croatian pattern:

• [something] + mi/ti/mu... + je + adjective

It is a useful structure to learn early.