NURBS are non-uniform rational B-splines and refers to a modeling method that employs curves and control points to define and manipulate surfaces. NURBS surfaces are computationally efficient and easily manipulated by the end user. NURBS are defined by four components: degree, control points, knots, and an evaluation rule.

From Wikipedia:

NURBS modeling – NURBS Surfaces are defined by spline curves, which are influenced by weighted control points. The curve follows (but does not necessarily interpolate) the points. Increasing the weight for a point will pull the curve closer to that point. NURBS are truly smooth surfaces, not approximations using small flat surfaces, and so are particularly suitable for organic modeling. Maya and Rhino 3d are the most well-known commercial software that uses NURBS natively.

A full explanation about the intricacies of NURBS can be found at: http://www.rhino3d.com/nurbs.htm or http://en.wikipedia.org/wiki/Non-uniform_rational_B-spline

Nurbs Curves

Controls points used to manipulate curves

Surface created from a loft across curves

Control points used to manipulate surface

Nurbs Modeling in Maya