The ozone layer protects us from UV light which comes from the sun! This UV light has three different bits in it. The first bit called UV-C is super harmful to all living things and is screened out completely. UV-B causes a lot of sunburn, and UV-A is mostly ok but lots of exposure can causes skin damage.
If there was no ozone layer, then we would expect to see a lot of eye problems, a lot of skin cancer and a lot of sunburn!