Parametric equations are equations where the coordinates of a curve are represented by functions of a variable (different from x or y of course) called parameter. Most examples you will see of parametric equations will use a parameter of t. They're important because they can provide a lot more data than a typical single equation and are often used to trace the motion of an object over a certain interval of time.
Hopefully you know what a unit circle (x^2 + y^2 = 1) is. The x coordinates on the circle are equal to the cosine of the inner angle while the y coordinates on the circle are equal to the sine that angle. So the parametric equation of the unit circle is: x = cos(t) y = sin(t)
A simpler example would be, let's say, f(x) = x+1. Making up a parametric equation for this would be simple. For example: x = t y = t+1
