Question

how do you appreciate the role of higher specific heat of water in stabilising atmospheric temperature during winter and sumer seasons

Answer 1

High specific heat means the substance takes a lot of heat to raise its temperature by 1⁰C. Also, water gives out a lot of heat when it cools by 1⁰C.

During winter water from oceans and rivers collects heat during the day and gives out during the night. The atmosphere gets warmed up in the night. It helps people from cold.

During summer because water takes a lot of time to heat up, water remains relatively cool compared to the atmosphere. That is why people swim a lot in pools and in rivers. 

Water evaporates taking a lot of heat and goes up into clouds. That evaporation keeps the water on surface and atmosphere cool. Breezes from the rivers, oceans blow towards the land due to the pressure difference (created by hotter temperature of air & lighter density)

Answer 2

Higher specific heat means the substance can absorb or discard high amount of energy with less change in its temperature. 
During summer, the water evaporates from rivers, ponds etc. by absorbing energy from atmosphere and water bodies. The evaporated water takes very high energy with it and hence leaves the atmosphere and the water bodies relatively at a lower temperature. So we get temperatures of both water sources and atmosphere relatively lower.