Why are there feathers on the end of a bow and arrow

Feathers on the back of the arrow shaft can be dispensed with.

The purpose of the feather is to adjust the flight of the arrow, to compensate to some extent for archer's mistakes and the effects of the natural environment.

The vast majority of archers around the world use them because there is basically wind when shooting arrows. There is no wind plus if the archer shoots the arrow perfectly, at 70 meters, the arrow won't be off.