This is the 10358th most frequent Russian word.
быта
"Быта" is not a standalone word in Russian; likely, you mean "быт," which translates to "daily life" or "everyday living."
Here, 'быта' is used in the genitive case to indicate the focus on aspects of everyday people’s life.
Вечером мы обсуждали вопросы быта.
In the evening, we discussed matters of everyday life.
In this example, 'быте' (instrumental case) is used to describe what the stories were about, i.e., village life.
Ее рассказы о быте в деревне были очень интересны.
Her stories about life in the village were very interesting.
The word 'быта' is used in the genitive case to indicate the topic under study, which pertains to modern everyday life.