Rain falls from clouds. But a cloud is not just white smoke. There are tiny water drops and sometimes small ice crystals inside a cloud. Most of them are too small and light to fall to the ground.
When small drops join other drops, they become bigger. In a cold cloud, ice crystals can grow too. They may melt into water as they fall through warmer air.
When a drop becomes too heavy, it cannot stay in the cloud. It falls from the cloud. If the air below is warm enough, the water reaches the ground as rain.