A very rough interpretation: Climate change puts more CO2 into the air. This traps heat into the air. This also allows more water into the air. Water is a great heat sink so it allows more thermal energy into the atmosphere.

All of this drives more extreme weather. Hotter summers, more extreme weather fluctuations, which leads to colder winters (hotter on average but can get more extreme), higher winds due to temperature disparity, and generally more precipitation. All of this drives more visible fluctuations like more and bigger tropical storms (hurricanes, typhoons), changes weather patterns leading to droughts, etc.

You can see trends for things like storms, wildfires, droughts, etc all going up.