In the past, it was a channel for people to travel across Seoul and it's still used for transportation purposes.
The Han River divides the north and south of Seoul so, in the past, it was difficult to travel between the two parts of the city. Over time, South Koreans built bridges to connect the north and south of Seoul. Now it's very easy to travel across the Han River.
Pollution in the Han River was a big issue before. People would dump chemicals and trash into the river. In 2006, a Korean movie called "The Host" (in Korean, Gwoemul) was made about a man-eating monster created by chemicals being dumped into the Han River. However, the government has since started programs to clean the river. The Han River provides drinking water to many Korean people, so it's important to keep it clean and safe.
In order for Korean people to travel across Seoul, sometimes they have to cross the Han River. In the 1990s there weren't many bridges so travel was oftentimes hard. However, over time, many bridges have been built so traveling across the Han River is easy and anyone can do it. There are a lot of bus routes and trains that pass over the river, so you don't even need a car.
