Bu yemin benim için önemli.

In Turkish, sentences like this often do not use an explicit verb in the present tense when the predicate is a noun or adjective.

So:

• Bu yemin benim için önemli = This oath is important to me / for me

Here, önemli is the predicate, and the idea of is is understood automatically.

If you were talking about the past or future, Turkish would show that more explicitly:

• Bu yemin benim için önemliydi = This oath was important to me
• Bu yemin benim için önemli olacak = This oath will be important to me

Bu means this.

It is a demonstrative adjective modifying yemin:

• bu yemin = this oath

Turkish does not have articles like a or the, so bu only adds the meaning this, not the.

Yemin usually means oath, vow, or solemn promise.

It comes from the idea of swearing or making a serious commitment. In different contexts, it can refer to:

• a legal oath
• a promise
• a vow

It does not mean a swear word in the English sense. For that, Turkish uses different words.

Because benim is the correct form used with için when the object is a personal pronoun.

• ben = I
• benim = my / for me in this structure

So:

• benim için = for me

This is the normal Turkish pattern with personal pronouns:

• benim için = for me
• senin için = for you
• onun için = for him/her/it
• bizim için = for us
• sizin için = for you all / for you formal
• onların için is possible, though onlar için is also common in actual use

So ben için would sound wrong.

İçin is a postposition that often means for.

So:

• benim için = for me

In this sentence, it shows whose perspective or concern is involved:

• Bu yemin benim için önemli = This oath is important for me / to me

A useful thing to notice: Turkish uses postpositions, which come after the noun or pronoun, not before it like English prepositions.

So English says:

• for me

Turkish says:

• benim için
• literally something like me-for

Because Turkish usually puts the predicate at the end of the sentence.

Here the predicate is önemli = important.

So the sentence structure is roughly:

• Bu yemin = this oath
• benim için = for me
• önemli = important

Turkish word order is often more flexible than English, but the most neutral version puts the main predicate last.

It is an adjective, meaning important.

But in this sentence it works as the predicate adjective, just like important in English:

• This oath is important

So önemli is still an adjective, but it is functioning as the main descriptive part of the sentence.

Yes. In natural English, important to me is often the best translation.

Turkish benim için önemli can correspond to:

• important to me
• important for me

Depending on context, English usually prefers important to me when talking about personal value or emotional importance.

So this sentence could naturally mean:

• This oath is important to me

Not exactly.

• benim için = for me, to me, from my personal standpoint
• bence = in my opinion

Sometimes they can be close, but they are not always interchangeable.

Compare:

• Bu yemin benim için önemli = This oath is important to me
• Bence bu yemin önemli = In my opinion, this oath is important

The first one stresses personal significance. The second one stresses your judgment or opinion.

Yes, but the emphasis may change.

The neutral order is:

• Bu yemin benim için önemli

You might also hear:

• Benim için bu yemin önemli

This puts more emphasis on for me.

Turkish allows this kind of movement more easily than English, but the most standard textbook order here is the original one.

In the present tense, third-person singular in nominal sentences usually has zero marking.

So:

• Ben yorgunum = I am tired
• Sen yorgunsun = You are tired
• O yorgun = He/she is tired

Notice that for o and for nouns, Turkish often uses no ending in the present tense.

The same thing happens here:

• Bu yemin benim için önemli = This oath is important

No extra ending is needed.

You would say:

• Bu yemin benim için çok önemli

Here:

• çok = very

So the structure becomes:

• Bu yemin = this oath
• benim için = to me / for me
• çok önemli = very important

A simple approximate pronunciation is:

• Boo yeh-MIN beh-NEEM ee-CHEEN uh-NEM-lee

A few sound notes:

• bu sounds like boo
• yemin has a y like in yes
• için has ç like ch
• ö in önemli is like the German ö or the vowel in French peu; English does not have an exact match
• Turkish pronunciation is generally regular, so words are usually pronounced much as they are written

The subject is bu yemin = this oath.

That is the thing being described.

The rest of the sentence tells us something about it:

• benim için = for me
• önemli = important

So the basic logic is:

• This oath → is important → to me

Not in this sentence, because here yemin is the subject and stays in its basic form.

So:

• bu yemin = this oath

If it were the direct object of another verb, it might change:

• Bu yemini duydum = I heard this oath
• Bu yemine inandım = I believed in this oath

But in your sentence, it is simply the thing being talked about, so no case ending is needed.