Imagine you have a big fan, and you're standing in front of it. The fan is blowing air at you and it feels nice and cool. Now, try to think of the Sahara desert as the fan and the surrounding areas as you standing in front of it.
The Sahara desert is the biggest hot, dry desert in the world, and it's located in northern Africa. In the summer, it gets extremely hot, and the air above it becomes very warm and rises up. When the warm air rises up, cooler air from the surrounding areas rushes in to fill the gap.
Now, this is where the "pump" comes in. As the cooler air rushes in, it picks up moisture from the surrounding areas and carries it into the Sahara desert. The moisture can come from the Atlantic Ocean or the Mediterranean Sea, or even from within Africa itself.
As the moisture gets carried into the Sahara, it causes more clouds to form above the desert. These clouds can lead to rain or just cover the sun, which helps to keep the desert cooler.
So, the Sahara Pump Theory says that the Sahara desert helps to create its own weather. By creating a cycle of warm air rising up and cooler air rushing in to fill the gap, the Sahara pumps moisture into itself and helps to regulate its own climate.
And that's how the Sahara Pump Theory works, like a big fan blowing cool air and moisture into the desert.