Questions & Answers about Moja siostra mówi, że ta sukienka jest ładna.
Because moja has to agree with siostra (sister), not with the speaker.
In Polish, possessive words like my change their form depending on the gender, number, and case of the noun they describe:
Since siostra is feminine singular, you use moja.
Siostra is in the nominative singular, which is the basic dictionary form.
It is nominative because it is the subject of the sentence:
- Moja siostra mówi... = My sister says...
A lot of feminine nouns in Polish end in -a in the nominative singular, and siostra is a typical example.