What is the effect of drag on an arrow and how does it affect the flight path?

Drag force causes a deceleration of the arrow proportional to the square of the arrow velocity. If there were no air, the only force on the arrow would be gravity and the result would be a parabola but the drag causes the arrow to slow down in flight so that it falls lower than it would with no drag.

The exact shape of the curve can be simulated but a good approximation can derived using a few reasonable approximations which are adequate for most practical purposes.