This is an important topic which is complex to write. I am attempting an answer to write on " What do you understand by Stability and Unstability of atmosphere". Kindly review.
The atmospheric stability and unstability depends on the difference between the lapse rate of the concerned air parcel and the lapse rate of the surrounding atmospheric environment.
The lapse rate of air parcel depends upon the presence of moisture. A dry parcel of air has lapse rate (DLR) around 9.8 degree celcius/km whereas completely saturated air parcel has lapse rate(SLR) around 4 degree celcius/km.
If the lapse rate of the environment surrounding the air parcel (ELR) is greater than the DLR, it means that the surrounding air gets cooled quicker than the air parcel. As a result, air parcel is warmer then the surrounding. Thus air parcel continues to rise. This condition is causes consant unstability.
On the other hand if ELR is less that SLR, then the air parcel will cool quicker than the surrounding air. It means that the air parcel at a particular altitude would be colder than the surrounding air at that altitude. Thus the air parcel sinks. This is the condition of Absolute Stability as air parcel is stable.
A third condition arises of Conditional Stability when ELR is more than SLR but less than DLR. In this case, the stability of air parcel depends on the adiabetic lapse rate of the parcel. If the LR of the parcel is more than ELR, it means the parcel cools more rapidly than environment. Such a parcel will remain stable unless the ELR remains less than the LR of the parcel. It must be noted that the Lapse rate of air parcel is dependent on the presence of moisture.
Stable and unstable atmosphere shapes other weather phenomenons such as rainfall, thunderstorms, etc.