Ozone layer, what it is and how does it work?

Greenhouse effect and ozone depletion are separate phenomenons, ozone depletion is caused as you stated by a chemical reaction of the ozone molecule (O3) with other molecules such as cfc (and also others) which results in the ozone degrading in molecular oxygen. The ozone works as a filter and prevents the uv radiation from reaching the surface. Uv radiation has nothing to do with greenhouse effect but is dangerous because it can cause physical harm to many living beings on earth, humans included. Greenhouse effect is caused instead by carbon dioxyde, methane and other chemical compounds that are transparent to sun radiation (that is so able to reach the surface) but reflectant to the infrared radiation coming from the earth. In this way the radiation coming from the sun reaches the surface, is absorbed by it. Then the radiation emitted from the surface is bounced back by the pollutants in the atmosphere and is readsorbed by the surface. This is exactly the same things that happens in a greenhouse with the glass taking the role of the co2. So basically both those phenomenons are environmental problems but they are uncorrelated since they are caused by different chemicals in different places of the atmosphere. And also the effects are different, greenhouse effect causes the average global temperature to incrase while ozone depletion allows dangerous uv radiations to reach the surface and its inhabitants.