Read this -> http://en.wikipedia.org/wiki/B%C3%A9zier\_curve
Pay particular attention to the animations midway down that page. You should understand how the curves are generated. There's a parametric formula given to you on that page to generate cubic curves, which is the curve commonly used. You can also combine multiple cubic curves together to form what is called a "Path". This is most useful for when you want to construct complex curves or even geometry. I recommend you use the pen tool in vector software such as Inkscape or Adobe Photoshop to get hands-on experience with curves. You can also use Blender to see how curves can be used to construct geometry.