Matcaps are weird, awesome, a hack, flexible and limited at the same time. The best thing with them is how darn fast they are.
Matcap stands for “material capture” and is a capture of a complete material — including diffuse color, lighting and reflections. It is really helpful while sculpting in 3D as you get useful feedback on a objects shape without having to light it or render it. They can look pretty darn good in realtime and even nicer when rendered.
They are mostly used as way to preview a model but they do fid their way into final animations and games from time to time. Rendering animations is pretty darn fast to render and in games it can be used to create effects (ghost/x-ray/etc.) and in games I’ve seen it used as a way to always keep the main character well lit even if it enters an area with small amounts of light.
A matcap is basically just an image (PNG/JPG/EXR/etc.) of a sphere with a material on it. As normals are used to mapp the sphere onto the model no UV-mapping or such need to be done, it just works.
I have built a librariy of matcaps and will upload them as soon as they have been saved into a good format to share.