Some people think the rider on a white horse is Christ, like in Revelation 19:11. But the only similarity between these two images is the horse. The four riders represent a destructive and senseless world. It has no redeeming qualities.
A bow is a weapon made of a curved piece of wood and a string. People shoot arrows with it. The bow was a common Greco-Roman military equipment. Here it is as a symbol of war.
to overcome and conquer: The repeated use of the Greek word nikaō (which means "conquer") shows this rider is powerful. The focus on war and conquest shows the deep sinfulness of humanity.