First, lets correct one error. The solar energy encounters a layer high in the atmosphere called the stratosphere where there is a gas called "ozone" which is a type of oxygen. There is not a zone called the "O-zone". The concentration of ozone in the ozone layer is actually quite small, only about 0.02 - 0.1 parts per million. If it was compressed down to sea-level pressure it would be about 3mm thick.

The ozone gas in this layer acts a bit like a layer of dust. The solar radiation hits it and some of it is absorbed. So less light energy from the sun can reach the surface. Unlike dust, this ozone does not absorb all types of light. The ozone layer is particularly famous for intercepting ultraviolet light (UV), which cannot be seen by our eyes, but which causes sunburns and damage to other things on the Earth's surface.

Oxygen gas in the atmosphere normally exists as 2 oxygen atoms. Each O2 molecule is a pair of O atoms because this gives it a lower energy state so it's more "relaxed". When sunlight hits the outer atmosphere the UV light adds energy to the O2 molecules and they split. But oxygen does not like to be all alone, so it immediately connects with another O2 molecule to form O3 which is ozone. These triangular ozone molecules also absorb UV light energy and use it to break apart the triangles and make pairs instead of triplets of O atoms. Hence the energy of the sunlight is reduced both by the formation and by the destruction of ozone in the ozone layer.