Annem börek için hamur açıyor.

My mother is rolling out dough for börek.

Breakdown of Annem börek için hamur açıyor.

• benim: my
• için: for
• anne: the mother
• hamur: the dough

Questions & Answers about Annem börek için hamur açıyor.

Why is annem one word, and what does the -m mean?

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

Why isn’t it benim annem here?

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.

What does börek için mean grammatically?

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.