In 2-d plotting, a parametric function is determined by a pair of parametric functions operating on a parameter. An example of a 2-d parametric function would be plot sin(t),cos(t) (which defines a circle).
For 3-d plotting, the surface is described as x=f(u,v), y=g(u,v), z=h(u,v). Therefore a triplet of functions are required. An example of 3-d parametric function would be cos(u)*cos(v),cos(u)*sin(v),sin(u) (which defines a sphere). It takes three parametric function specifications in terms of the parametric dummy arguments to describe a single graph.
The total set of possible plots is a superset of the simple f(x) style plots, since the two (three) functions can describe the x and y (and z) values to be computed separately. In fact, plots of the type t,f(t) (u,v,f(u,v)) are equivalent to those produced with f(x) when the x values are computed using the identity function as the first function.
Note that the order the parametric functions are specified is xfunction, yfunction (and zfunction) and that each operates over the common parametric domain.
Also, the set parametric function implies a new range of values. Whereas the normal f(x) and f(x,y) style plotting assume an xrange and yrange (and zrange), the parametric mode additionally specifies a trange, urange, and vrange. These ranges may be set directly with set trange, set urange and set vrange, or by specifying the range on the plot or splot commands. Currently the default range for these parametric variables is [-5:5]. Setting the ranges to something more meaningful is expected.