The "graying of America" refers to the increasingly elderly population around the start of the 21st century. At that time, there was a large increase in the elderly population as a percentage of the country's population as a whole.
Having a large elderly population presents a variety of challenges for other citizens and the government. As most elderly are retired workers, they rely on pensions and Social Security to survive, which both drain government resources. Many cannot afford to live in homes with assisted living or nursing options, so they are forced to live with their children, who may be approaching retirement age themselves. The term "graying" refers to the typical hair color that develops as humans age.