Questions & Answers about Я доварила рис, пока мама накрывала на стол.
Доварила comes from доварить, which means to finish cooking or to cook something until it is done.
The prefix до- often adds the idea of bringing something to completion. So:
- варила рис = was cooking rice / cooked rice
- доварила рис = finished cooking the rice
In this sentence, the speaker is not just describing the process. She is saying that she completed the rice-cooking.
That is the past tense feminine singular ending.
In Russian past tense, verbs agree with the subject in gender and number:
- я доварил = I finished cooking it (said by a man)
- я доварила = I finished cooking it (said by a woman)
- мы доварили = we finished cooking it
So я доварила tells you that the speaker is female.
The same thing happens in мама накрывала: мама is feminine, so the verb is feminine too.