Domestic generally means relating to someone's family, home, or home country. Domestic work is work done in the home — a domestic is someone who works in a home, such as a nanny or a maid.
Domestic is also used to refer to products that are produced in your country, or policies and affairs that relate to your country. And domestic animals, such as cats and dogs, are used to living with people. Domestic derives from Middle English, from Old French domestique, from Latin domesticus, from domus, "house."