All storms have two things in common: low atmospheric pressure at the storm’s center, and winds that are created by the flow of air from higher pressure outside the storm toward the low pressure at the center.
Wind, in other words, is air that’s being pushed by high pressure toward low pressure.
Areas of low air pressure occur because the Sun heats the Earth unequally.
The Sun shines down almost directly on Earth’s tropical regions near the equator, heating this region more than the polar regions around the North and South poles and the middle latitudes between the poles and the tropics.
Storms, along with ocean currents, redistribute heat from the tropics to the middle latitudes and the poles. Without storms and ocean currents, the tropics would grow hotter and hotter until the oceans boiled.

In other words, the Sun’s heat powers the weather.

Air pouring into an area of low pressure from all sides rises because it doesn’t have any place else to go.
As air rises, it cools, and if it cools enough the water vapor in the air begins to condense.

This condensation creates the tiny drops of water or tiny ice crystals that make up clouds.
Under the right conditions, the tiny water drops or ice crystals merge to fall from the cloud as larger water drops of rain or ice crystals of snow. This is why storms bring clouds and usually bring rain, snow, or other kinds of ice.
The University of Illinois Weather World 2010 Project’s Clouds and Precipitation Web page provides detailed information on how this works.