How have they been used and how do they damage the ozone layer?
The Usefulness of Their Features
Chlorofluorocarbons also known as CFCs for short, are halocarbons which means that they contain carbon and halogen atoms in the compound. As you can tell from the name, these halocarbons comomntain the halogens Chlorine and Fluorine. These are used as solvents as well as used to make aerosols, blowing agent for foams and the unnecessary packaging material you always find in your Amazon delivery box. There is no need to worry as CFCs are non-toxic and non flammable. This is how to work out the formula of a CFC molecule:
You add 90 to the CFC number to give a new number. For example, CFC-11 generates the number 101 (11+90)The first digit of the new number tells you how many carbon atoms there are. The second number tells you the number of hydrogens, and the third the number of fluorines. You calculate the number of chlorines from the formula Cl = 2(C+1)-H-F 
Before CFCs were used as refrigerants, companies were using toxic gases such as ammonia, methyl chloride and sulfur dioxide. These was used until there were a series of accidents where the chemicals leaked out of the fridges. They had to find less toxic replacements and so Thomas Midgley synthesized CFCs as a safer chemical for refrigerators. This is where the non toxic features of CFCs came in handy. From there one all the new refrigerators used CFC-12, when companies found out how useful CFCs were they started to be used in air conditioners in public buildings. Later on after WWII, the CFCs started to get used as insect propellants, paints, hair conditioners and other health care products. This started a CFC craze in industries all over the world, CFCs were being used in cars air conditioning, in homes and office buildings. It was the fact that the CFCs were so stable, non toxic and volatility that made them so popular and useful. They were unaware of dangers of this chemical craze.
The Second Face of CFCs
When CFCs are used they go into the atmosphere, the wind mixes them well in troposphere (lower atmosphere the air we breathe), they are harmless in this atmosphere as the CFCs are very stable, its because of this stability so they don't dissolve in rain. After a few years they rise to there next atmosphere up, the stratosphere where there they are exposed to strong UV rays. The UV rays cause homolytic fission on the CFCs, creating highly reactive chlorine radicals.
The chlorine radicals are able to destroy the ozone (O3) because they works as catalysts in the the breakdown of the ozone molecule. Once it splits up the ozone molecule to create ClO (chlorine oxide). This molecules then combine to the freed oxygen to create two oxygen molecules. This kick starts a chain reaction and the chlorine will destroy thousands of ozone molecules. Since the ozone is broken down it can no longer absorb the UV rays coming from the sun and so they get through to the earth therefore heating it up even more along with issues that it can cause us too such as skin cancer.
Here is the reaction to show the breakdown of the ozone molecules:
Cl + O3 → ClO + O2
ClO + O → Cl + O2
O3 + O → 2O2 : Overall reaction 
Here's a diagram to show this process