If instead of clicking two points with the pen tool you click+hold something different happens. The line will appear to propagate from the center. This line isn't a line at all, but instead is a set of "handlebars"(they allow you to steer the line).

Click+ hold to create a set of handlebars, then release and move the mouse around, you will see a curved line appear. (image 1)

The curvature of this line is determined by the length and angle of the handlebars.

As you continue to draw this line the same rules apply, click and hold to build handlebars, then draw the line. If you want a straight just click then click where you want the next point.

You can adjust the handlebars (therefor the curvature) after a line is drawn. Just click the anchor point you want to work with using the direct selection tool and the handlebars will appear. If you use the selection tool the adjustments will be symmetric, if you use the direct selection tool the adjustments will be asymmetric.

The other tool hidden behind the pen tool is the anchor point tool, it is used to add or remove anchor points.

The tool below the pen tool is the curvature tool. It will allow you to draw curves and AI will attempt to make them as fair as possible. (Image 2). It is faster at making curves than the pen tool but also less precise.

If you click the curvature tool while working with lines from the pen tool it will automatically switch over to curves.