The window "Domain" displays a domain as a wireframe, a point (u0, v0) in the domain, and the u-constant and v-constant curves through that point in red and green, respectively.

The window "Surface X(u,v)" shows the cone X(u,v) = (av*cos(u), bv*sin(u), cv) for the given domain, the images of the point and the curves from the "Domain" window, and the tangent vectors Xu(u0,v0) and Xv(u0,v0) to the surface at the point X(u0,v0).

Checking the "Show tangent plane" checkbox will show the tangent plane to X(u,v) at the point X(u0,v0). Note that the tangent plane is not defined at the vertex (0,0,0) of the cone because that point is not a regular point.