Annem bugün bana dargın değil, sadece biraz üzgün.

Annem means my mother.

It is built from:

• anne = mother
• -m = my

So:

• anne = mother
• annem = my mother

This -m is a possessive ending. Turkish often attaches possession directly to the noun instead of using a separate word like my.

Because dargın olmak takes the person with the dative form, not the direct object form.

• ben = I
• bana = to me
• beni = me

In Turkish, birine dargın olmak means to be offended with someone / to be on bad terms with someone.

So:

• bana dargın = offended with me / upset with me

You would not normally say beni dargın here, because dargın does not take a direct object.

Dargın usually means something like:

• offended
• hurt
• not speaking warmly to someone
• a little resentful toward someone

It is often used when a person is emotionally distant from someone because of something that happened.

This is slightly different from kızgın, which usually means angry.

So:

• bana kızgın = angry with me
• bana dargın = upset with me / offended with me / not warm toward me

Dargın often sounds softer and more relational than kızgın.

Yes. Değil is the usual way to negate noun and adjective sentences in Turkish.

Since dargın is an adjective, Turkish makes it negative with değil:

• dargın = upset / offended
• dargın değil = not upset / not offended

This is different from verb negation, where Turkish usually uses a suffix:

• geliyor = he/she is coming
• gelmiyor = he/she is not coming

But with adjectives and nouns:

• mutlu = happy
• mutlu değil = not happy

So in this sentence, değil works very much like English not.

In Turkish, the present tense form of to be is often not expressed as a separate word in simple statements.

So:

• Annem üzgün. = My mother is sad.
• Annem dargın değil. = My mother is not upset/offended.

Turkish does not need a separate word like English is in these present-tense adjective sentences. The idea of is is understood.

That is why the sentence can simply say:

• Annem ... dargın değil
• ... biraz üzgün

without an extra verb.

Yes, bugün can move around, because Turkish word order is flexible.

Here:

• Annem bugün bana dargın değil.

This is a very natural order: My mother today is not upset with me.

You could also hear:

• Bugün annem bana dargın değil.
• Annem bana bugün dargın değil.

These all make sense, but the emphasis changes slightly.

Very roughly:

• Bugün annem... puts more focus on today
• Annem bugün... sounds neutral and natural
• Annem bana bugün... can make today sound a bit more contrastive

So the sentence uses a normal, natural placement.

Because Turkish often leaves out words that are already clear from context.

The full idea is:

• Annem bugün bana dargın değil, sadece biraz üzgün.

The second part still refers to annem, so Turkish does not need to repeat it.

You could expand it as:

• Annem bugün bana dargın değil, sadece biraz üzgün.
• understood as: Annem ... sadece biraz üzgün.

This is very normal. English does something similar too:

• She’s not mad at me, just a little sad.

So the second clause is shortened because the subject is already understood.

It is another adjective phrase describing annem.

• sadece = only / just
• biraz = a little / a bit
• üzgün = sad

So the structure is:

• sadece modifies the whole idea: just
• biraz modifies üzgün: a little sad

Together:

• sadece biraz üzgün = just a little sad

This gives a softer contrast after dargın değil: she is not upset/offended, only a bit sad.

Because biraz works like an adverb here and modifies the adjective üzgün.

• üzgün = sad
• biraz üzgün = a little sad

This is the normal order in Turkish: the degree word comes before the adjective.

Other examples:

• çok mutlu = very happy
• biraz yorgun = a little tired
• fazla ciddi = too serious

So biraz üzgün is exactly the expected pattern.

This is a very common learner question.

• üzgün is an adjective meaning sad
• üzülmüş literally comes from the verb üzülmek and often means has become sad / looks saddened / seems upset

In many situations they can be similar, but the feeling is a bit different:

• üzgün = a general state
• üzülmüş = a more result-like or event-related feeling

In your sentence, üzgün sounds simple and natural: it describes her emotional state.

Değil is often tricky for learners because of ğ.

A rough pronunciation is something like:

• deyil or dee-il, depending on accent and speed

Important point:

• ğ usually is not pronounced as a strong consonant like g
• it often lengthens the previous vowel or creates a slight glide

So değil is not pronounced like degil with a hard g.

In slow careful speech, learners often approximate it as:

• de-yil

That is usually close enough to start with.

Yes.

Without bugün, it becomes a more general statement:

• Annem bana dargın değil, sadece biraz üzgün.

With bugün, the sentence is anchored specifically to today. That can suggest:

• this is her mood today
• maybe it is temporary
• maybe she is not generally upset with me, just today she seems sad

So bugün adds time context and can make the sentence feel more situational.

The comma separates two contrasting parts:

• Annem bugün bana dargın değil
• sadece biraz üzgün

This is similar to English:

• She isn’t upset with me, just a little sad.

The comma helps show the pause and contrast: not X, only Y.

It is not the most difficult grammar point here, but it makes the sentence easier to read and understand.