Age limit: in some areas, the hairdressing industry has certain restrictions on the age of apprentices, who need to be within the age range stipulated by law to engage in apprenticeships. The boss may need to confirm whether your age meets the requirements.
Family background: the boss may need to know your family background, including family situation, family economic situation and so on. So as to know whether you are suitable for apprenticeship.
Work attitude: The boss may want to interview you and your mother to find out your work attitude and willingness, as well as your work ability and quality.
In a word, the boss asked for an interview with your mother out of consideration for his apprentice and requirements for the quality of work in the hair salon. If you are interested in apprenticeships, you can go to your mother for an interview and learn more.