How do convection cells in earth's atmosphere cause high- and low-pressure belts?
The Earth's atmosphere follows a specific pattern of circulation due to the tilt of the Earth causing varying amounts of solar radiation to reach different locations which in turn affects atmospheric circulation.
More specifically, at the Equator the rays of solar energy are most direct and the air gains thermal energy causing its molecules to expand--warm air rises because it is less dense than cooler air. It eventually cools and cooler air with molecules that are closer together are more dense and will therefore sink. This process is known as convection. Warmer moist air has less pressure than cooler dry air.
Much of this air will recirculate again in the same way however, some will split into two directions heading towards the poles. Eventually, the air sinks at 30 degrees N and S latitudes and this air splits into two directions once again. This pattern occurs at the higher altitudes of the tropopause (top of the troposphere) because warmer air rises. At the poles, where the air is cool and more dense, it will sink as warmer less dense air rises and it will flow toward 60 degrees latitude N and S.
In this way, thermal energy from warm air near the Equator is transferred towards the Poles and cool air from the Poles cools the areas it passes over. This is how the Earth's temperatures are moderated via the process of atmospheric circulation.