The notion of gender socialization involves how gender is perceived by society. Part of this involves the expectations that social orders place on genders. In different parts of the world, the mere label of "boy" or "girl" carries with it a great deal of social weight and certain conditions that are dictated by society. At an early age, being able to play with dolls or play with trucks are mere examples of how this socialization happens through gender bias and perception. Gender socialization transpires through how society views the roles and purposes of each sex and its study involves these implications on people. Studying it in the childhood stages reveals a great deal about who we are as a society and what is expected from genders. For example, years ago, a group was able to infiltrate production of Barbie Dolls and G.I. Joe action figures and within each spoken version, the statements were inverted. The G.I. Joe action figures spoke statements about "tea parties" and "inviting boys over for partying" while the Barbie dolls spoke of military operations and determining manners of leading a specific offensive mission. This would be one example in how gender socialization presents itself in the most "innocent" of circumstances.
Socialization is the process by which kids learn the values of the culture in which they live. Kids are socialized first by their parents and then later by friends and teachers. In many societies, the different genders are expected to behave quite differently -- this is a value in such societies. So gender socialization is the process by which a kid is taught how his or her gender is "supposed to" behave.
For example, a child might be taught that "boys don't cry" or that girls don't play rough games. These sorts of socialization play a large role in setting up gender stereotypes and attitudes that persist later in life.