Ozone is the triatomic oxygen molecule O3. It is an extremely powerful oxidant and is a serious respiratory hazard to humans so we do not want ozone to be present in the lower atmosphere. Ozone does, however, very effectively absorb ultraviolet radiation from the Sun, particularly in the UV-B range (280-315 nm in wavelength). This is the radiation that can cause sunburns and damages skin. So the ozone layer in the upper atmosphere is incredibly important to life on Earth by filtering out this harmful natural radiation from the Sun.
Ozone is actually an unstable molecule, and it eventually breaks down into molecular oxygen (O2) and an oxygen radical (an oxygen atom with a free unpaired electron). This degradation process is slow in the cold temperatures of the upper atmosphere but nonetheless it does still constantly occur. Fortunately, there is also a process by which ozone is constantly regenerated in the atmosphere as well. UV light from the Sun will slowly break down a molecule of O2 into two oxygen radicals. An oxygen radical can then combine with a new molecule of O2 to produce ozone (O3). This constant cycle of breakdown and regeneration of ozone is called the ozone-oxygen cycle and it is what prevents the ozone layer from depleting naturally. This is why chlorofluorocarbons (CFC's) from aerosol cans are so harmful to the ozone layer. They introduce different chemical radicals into the atmosphere, thus disrupting the ozone-oxygen cycle and preventing new ozone from being produced.