A pcurve is a parameter curve which is created on a surface when the surface is limited.
A pcurve is used to define the trim boundary of a surface and is made up of a series of line segments which match the surface to within tolerance. A pcurve is a parameter curve because the curve is defined in the 2D parameter space of a surface. A pcurve contains points which are called ppoints. Every surface is defined by parameters t and u which vary across the surface.
The values of t and u uniquely define a point, p, on the surface. Thus, point p can be defined by 3D world space coordinates (x, y, z) or by 2D parameter space coordinates (t, u). In the figure below, the 2D parameter space coordinates of p are (3.5, 2.75).
World coordinates are not guaranteed to lie on the surface, whereas parameter space coordinates must, by definition, lie on the surface (the third dimension is the surface). Curves used as part of trim boundaries of surfaces must lie exactly on the surface being trimmed, and so pcurves are defined within the 2D parameter space of a surface. They cannot therefore be operated on in quite the same way as other curves (for example, they cannot be dragged off a surface) and a special editor is provided to manipulate them.