Hi Alex,
That's an interesting question. The Earth's ozone layer protects us from much of the ultraviolet (UV) radiation from the Sun. the UV radiation from the Sun is what causes us to get a sunburn if we stay outside too long and do not wear sunscreen. If our atomosphere did not have an ozone layer, more UV radiation would reach the Earth's surface. This would probably make people sunburn much faster and cause an increase in skin cancers.
The ozone layer does not specifically play a role in protecting us from solar activity like solar flares and coronal mass ejections. The main danger from solar storms, such as solar flares, are the energetic particles associated with these events. Fortunately, the Earth's magnetic field, or magnetosphere, helps to protect us from the most dangerous effects of solar flares. However, satellites orbiting the Earth can be damaged by the geomagnetic storms that are caused by coronal mass ejections and solar flares. Solar storms would also pose a serious health risk to astronauts traveling to Mars as they would have to leave our protective magnetosphere.
Kris