First of all, atmosphere consists of various gases like oxygen, carbon dioxide, nitrogen, etc. Oxygen is inevitable for the existence of most of living organisms.
Secondly, earth gets heated by the rays of sun. When it radiates this heat, some atmospheric gases like carbon dioxide trap this heat and keep the earth warm. This effect is called Greenhouse Effect. This keeps the average temperature on earth sufficiently warm to sustain life.
Then, the atmosphere also contains the ozone layer in the stratosphere. The ozone layer absorbs the harmful ultraviolet rays of the sun. Thus, the atmosphere protects the life on earth from the harmful UV-rays.
Moreover, when meteors enter the atmosphere, they burn off due to friction. Most of the meteors burn up before reaching the surface. In this way, the atmosphere also protects us from the meteors.
In all these ways, atmosphere helps to sustain life on earth.