The most important effect of Chlorofluorocarbons (CFCs) on the atmosphere, and the one that most people know about, is its role in reducing the atmospheric ozone layer. The ozone layer protects the Earth from harmful Solar radiation, including ultraviolet radiation, which can cause skin cancer and harm plants, animals, and bacteria. Once public concern began to grow, government took steps to reduce and then ban CFCs from commercial products and industrial uses.
The second major effect, less well-known because of diminished CFC production, is in the greenhouse effect. CFCs are one of several gasses that collect in the atmosphere, thickening it and helping to contain more heat energy from the Sun. The effect is like a glass greenhouse; heat from outside enters, reflects off the Earth's surface, and then can't leave because it reflects again off the thicker atmosphere.
Both these effects are negative overall for the Earth's ecosystem and living population.