What is the process by which boys and girls internalize their culture's norms, sanctions, and expectations for members of their gender?

Sex - Role Socialization.

Explanation:

Sex - Role Socialization refers to the focus on the development of male and female psychological characteristics and the implications of that development for participation in social roles. It is a process that maintains sex type behavior throughout life. Establishing "appropriate" sex-role identification during early childhood was seen as critical to the later sexual, psychological functioning of an individual.