A drainage system is like a big puzzle made up of tiny pieces. Every time it rains, tiny droplets of water fall on the ground and they flow towards bigger droplets of water. These bigger droplets of water make up things like rivers, lakes, streams, and oceans.
Now, imagine a mountain. When it rains on a mountain, the tiny droplets of water take different paths down the mountain, based on how steep that area is. They may end up joining together into a stream, and eventually into a river.
Now, when we talk about a drainage system in a geomorphology sense, it means all the streams, rivers, lakes and oceans that collect water from a specific area, like a watershed. A watershed is just a fancy word for the area of land where all the water that falls within it flows out to the same location (usually a river or a lake).
The drainage system of a watershed tells us how the water flows through it. Different types of waterways can have different types of drainage systems. Some can be dendritic, which means they look like the branches of a tree, where tributaries join larger streams and eventually lead to the main river. Others can be parallel, where river channels run relatively straight, with minor tributary channels joining into them. They could also be rectangular, where channels are approximately rectangular in shape.
In a nutshell, a drainage system is a way to study how water flows through a particular area of land. By understanding how the water in a particular drainage system moves, we can predict things like floods and other natural disasters, better manage the water supply, and protect our environment.