The simple explanation is that raindrops can actually attract aerosol particles as they fall. An aerosol is a collection of tiny pieces of something in the air, like a cloud. Fog, dust, smoke, and air pollution are all examples of aerosols that are made up of water droplets or little bits of dirt and other materials. As a raindrop falls from the sky, it attracts these particles, which stick to and become part of the raindrop. When it rains, every single raindrop collects some of the pollution particles in the air so that all the raindrops working together actually help to clean the atmosphere. This is why the air is clearer and we can see the mountains after it rains.
Unfortunately, all the pollution still has to go somewhere. Those tiny pieces of dirt and chemicals that are now attached to the raindrops end up in the water that floods the streets and soaks into the ground when it rains. The rain also washes dirt and chemicals from the streets and people's lawns and homes into the nearby waterways, including lakes, rivers, and (eventually) the ocean.
The chemicals and pollution that wash into the rivers and the ocean can really hurt the animals and plants that live there, and make them very unhealthy. This includes fish and other sea creatures that we eat, which is a big deal here in Chile because Chileans eat a lot of seafood! You may not realise that driving your car too much would affect the sushi you are going to have for lunch, but everything is connected.
This is a problem in the United States, too. Even places without much air pollution, like the small town in New Hampshire where my family lives, can have problems with chemicals running into the river when it rains.