According to the BBC, boys grow taller than girls due to the growth spurt delay boys experience during puberty, adding two more years of childhood growth. Additionally, boys grow at a faster rate during this growth spurt due to the effects of testosterone, which prompts cells to grow.
As the BBC states, testosterone is responsible for other skeletal and muscular related changes within the growing boy's body. The shoulders and chest become broader. Bone structure overall becomes much denser and stronger. Muscle fibers become longer and wider. Testosterone also triggers red blood cells to deliver more oxygen to muscles through the increase of hemoglobin levels.