When officers ride on a horse, they can sit higher up than everyone else. This helps them see over the people in a crowd like how a tall tree can see over small bushes. Since they are up high, they can also move around easily and have a better view of everything happening.
Imagine you are in a playground, and everyone is playing. If you stand on a big slide, you can see your friends better than if you were on the ground. The officers on horses can see more things and help keep everyone safe, just like you can see your friends from the slide!