The layer of the Earth's atmosphere that is impacted by chlorofluorocarbons or CFCs is the stratosphere.
"The stratosphere is the second major layer of Earth's atmosphere, just above the troposhphere, and below the mesophere."
CFCs were developed in the early 1930s and were used in a variety of industrial, commercial, and household applications. It was not until 1984 that the damage from CFCs was conclusively linked to ozone depletion.
Ozone in the stratosphere is important becasue it acts as a primary UV radiation shield. Without this shield more UV radiation is making its way through our atmosphere and impacting humans.
"It is suspected that a variety of biological consequences such as increases in skin cancer, cataracts, damage to plants, and reduction of plankton populations in the ocean's photic zone may result from the increased UV exposure due to ozone depletion."