Instead of using a single equation to generate a curve, two parametric equations are used. One equation generates the x-coordinate of each point, the other generates the y-coordinate.
Here the letter t denotes the parameter, and the x- and y-coordinates are calculated from formulas involving t.
You'll see various values of t marked on the curve, at the points they generate.

You'll also see the parametric equations in the form (X(t), Y(t)), where X(t) and Y(t) are functions of t.
You can vary the values of a, b or c by clicking the buttons at the bottom. Not all of them work at the same time, but you can tell which to click from the equations of the curve you have chosen.
Play around - enjoy yourself!