NURBs (non-uniform rational bezier splines) are an efficient computational way of representing standard objects (spheres, cones, boxes etc) and complex surfaces like airplane or car bodies. They work by interpolating a curve through a list of control points. Because complex shapes can be described with a mathematical formula and a short list of coordinates they are a more efficient way of describing geometry than with large numbers of tiny triangles (meshes). Rhino is primarily a NURBs modelling tool. See Rhino's documentation for an in depth explanation.
Meshes describe geometry using lists of points (or vertices) and faces (or polygons) connecting points to represent surfaces. If your geometry is non-planar or contains a lot of fine detail, a very large number of vertices and faces will be needed to describe all of this geometry without it appearing as a faceted approximation. Meshes are used to draw (or render) geometry to your display by simulating how light reflects from these polygonal surfaces. Fologram uses meshes to display geometry on the HoloLens.