Annem börek için hamur açıyor.

Annem is made from anne + -m.

• anne = mother
• -m = my

So annem means my mother / my mom.

In Turkish, close family words often take a possessive ending directly, so you do not need to say benim annem every time.
Both are possible:

• annem = my mom
• benim annem = my mom with extra emphasis, like my mom in English

Because Turkish often leaves out the separate possessive pronoun when the possessive ending already shows the meaning.

So:

• annem already means my mother
• benim annem is more explicit or emphatic

In normal everyday speech, annem is very natural and common.

İçin means for.

So börek için means for börek or for making börek.

This is a very common pattern in Turkish:

• çay için su = water for tea
• misafir için yemek = food for guests
• börek için hamur = dough for börek

Here için shows purpose.

Because için usually follows the basic noun form when you mean for X in a general purpose sense.

So:

• börek için = for börek
• çorba için = for soup
• tatlı için = for dessert

You do not need an accusative ending here.

Yes, açmak very often means to open, but Turkish verbs can have idiomatic uses.

With hamur, yufka, or similar food-related words, açmak means:

• to roll out dough
• to flatten/spread dough with a rolling pin

So hamur açıyor does not mean she is opening dough in a literal English sense. It is the normal Turkish expression for preparing dough in this way.

Because here hamur is an indefinite direct object.

In Turkish:

• hamur açıyor = she is rolling out dough / some dough
• hamuru açıyor = she is rolling out the dough / a specific dough we already know about

This is a very important Turkish pattern:

• bare object = indefinite, non-specific
• accusative-marked object = definite or specific

So the sentence sounds like a general statement about what she is making, not about one already-identified dough.

Yes. That would be grammatical, but it changes the nuance.

• Annem börek için hamur açıyor = My mom is rolling out dough for börek.
  Focus: the activity in general.

• Annem börek için hamuru açıyor = My mom is rolling out the dough for börek.
  Focus: a specific dough, probably already known in the conversation.

So both work, but they are not exactly the same.

Açıyor comes from açmak and uses the -yor tense marker.

Structure:

• aç- = verb stem
• -ıyor = present continuous marker

So açıyor means:

• is rolling out
• is opening
• sometimes simply rolls out, depending on context

In this sentence, the most natural meaning is is rolling out.

Because Turkish vowel harmony affects the form of the -yor tense.

The progressive marker is often taught as -yor, but in practice the vowel before it changes:

• geliyor
• bakıyor
• görüyor
• duruyor

With açmak, the form becomes açıyor.

So the vowel is ı, not i.

Yes. Although -yor often means is doing, it can also be used for:

• actions happening around now
• temporary situations
• sometimes habitual or current real-life activities

So Annem börek için hamur açıyor could mean:

• she is doing it right now
• she is currently in the process of making it
• in context, even something like Mom is making dough for börek

Context tells you how immediate it is.

Turkish word order is flexible, but the neutral order is often:

Subject + other elements + verb

Here:

• Annem = subject
• börek için = purpose phrase
• hamur = object
• açıyor = verb

The verb usually comes at the end in a normal statement.

So this sentence has a very natural Turkish word order.

Yes, Turkish allows reordering for emphasis, but the verb usually stays at the end.

For example:

• Annem hamur açıyor börek için
• Börek için annem hamur açıyor

These can be grammatical in the right context, but Annem börek için hamur açıyor is the most neutral and standard version.

Word order changes emphasis more than basic meaning.

No. The direct object of açıyor is hamur.

She is rolling out dough, not börek.

Börek için is a purpose phrase meaning for börek.

So grammatically:

• hamur = object
• börek için = purpose expression

A simple approximate pronunciation is:

AHN-nem BUH-rek ee-CHEEN hah-MOOR ah-CHUH-yor

A few useful notes:

• ö is like the vowel in German schön or French peu, not a plain English o
• ü is not in this sentence, but börek has ö
• ç is pronounced like ch
• ı is a vowel English does not really have; it is a dull, back vowel, not ee

A more natural syllable breakdown:

• An-nem
• bö-rek
• i-çin
• ha-mur
• a-çı-yor

Anne is the normal everyday word for mother/mom.
Depending on context, annem can sound like:

• my mother
• my mom

So in many situations, my mom is the most natural English feel.

It is not unusually formal. It is a very common family word.

The dictionary form is açmak.

Turkish dictionaries usually list verbs in the -mak / -mek infinitive form.

So:

• açmak = to open / to roll out
• açıyor = is opening / is rolling out

When learning vocabulary, it is best to remember the base form as açmak, but also learn common expressions like hamur açmak as a chunk.