This tutorial explained how a line in Illustrator is defined by two anchor points, shown in the upper left image. If you were to use control handles that extend off from anchor points, they will control how the curves are drawn from point to point. You can see this exampled in both the images on the right. In the top right side image, the anchor points are the same as the anchor points as the line on the left, but the control handles dictate taht the line is not straight from one point to the other.

this is from the tutorial page http://www.lynda.com/home/DisplayCourse.aspx?lpk2=351 >>> "understanding paths" link