Bezier curves are parametric curves which are plotted by control points. They are used in computer science in order to plot curves and make timing-function for animations. In mathematics side, they are constructed by using Bernstein polynomials. Bezier Curves are widely published by Pierre Beziẽr and who used them for automobile design. For more information see Wikipedia article.

I have made a tool with HTML5 that gives ability to play with bezier curves by putting and transforming the points on the screen. When you added a point, it increments the degree of Bernstein Polynomial.

Wolfram Mathworld have more information about its mathematical background, you can see here.

Click to play with Bezier Curves