There are several advantages that parametric equations have over rectangular equations.

1) On the rectangular equations graph the arrows indicate that the graph is continuing on in the established fashion. On the parametric equation, the arrows indicate the direction an object would move along the path as the parameter increases.

Parametric equations show both horizontal and vertical position of an object over time, while rectangular equations can only show one or the other.

2) Parametric equations are used to define curved lines or surfaces. A set of numeric values will give you a point in space, but wont give you the shape of the curve.

3) Another advantage of parametric equations is  the equations comes from there utility in three dimensions. If we want to write the equation of a curve in three dimensions, the rectangular  approach fails completely.

Parametric equations show both horizontal and vertical position of an object over time, while rectangular equations can only show one or the other.