Curve casts are casts that have a bend in the line to the right or left of you. They can be useful for casting over fast water to get to slower moving water. The fast water that is closer to you will end up pushing your fly downstream too fast. A curve cast will add some slack in the line that will keep your line in the faster current above the line in the slower current. Curve casts also work well for presenting your fly around surface objects.
