Learn Hardcore Greek: Η αδερφή μου τραγουδάει πολύ καλά και θέλει να γίνει μουσικός. - My sister sings very well and wants to become a musician.

Η is the definite article “the” in the feminine nominative singular. In Greek, you normally use the article with a noun even when there is a possessive pronoun like μου.

So Η αδερφή μου is literally “the sister of mine”, which corresponds to my sister.
Leaving out the article (Αδερφή μου τραγουδάει…) is possible in some contexts (for example as a form of address: Αδερφή μου, έλα εδώ! – My sister, come here!), but for a normal statement about a specific person, native speakers strongly prefer Η αδερφή μου.

Why is it αδερφή μου and not μου αδερφή, like in English my sister?

In Greek, the unstressed (enclitic) possessive pronouns like μου usually come after the noun they modify:

η αδερφή μου = my sister
ο αδερφός σου = your brother
το βιβλίο του = his book

You cannot put μου before the noun the way English does (my sister). The “normal” order is article + noun + possessive pronoun: η αδερφή μου.

If you want to emphasize possession, you can use stressed forms like δικιά μου:

η δικιά μου αδερφή = my own sister / my sister (as opposed to someone else’s)

But μου αδερφή is not correct.

I’ve seen αδελφή instead of αδερφή. What’s the difference?