* Rain washes out dust: Rainfall acts like a giant cleaner for the atmosphere. Raindrops collide with dust particles, making them heavier, and pulling them down to the ground. This leaves the air clearer, which is why the sky often looks brighter and more blue after a rain shower.
* Clouds dissipate: Clouds are made of water droplets or ice crystals. As rain falls from a cloud, it removes some of the water vapor that makes up the cloud. Additionally, the downdraft of air associated with rain can help to disperse the cloud. This is why clouds often appear to disappear or shrink after a rain shower.
So, while rainfall doesn't directly make the clouds disappear, the rain process itself does contribute to the dissipation of the clouds.