Off-the-cuff attempted description of Tensor Fields that came up in a conversation.

   Basically - imagine kind of an arrow at every point in space that describes some force at that point (maybe a bathtub draining, and each arrow is the direction and strength that water is flowing at that point). This is called a vector field. a tensor field is that, but the arrows indicate some other property of space at that point, for example, one could talk about a tensor field (the tensor field is the term for the collection of all of these arrows) that describes the stretching forces on a rubber band as you stretch it. They can also describe curvature of space itself - when Riemann first published about them they were considered very abstract and useless to any real world thing. When Einstein was formulating the theory of General Relativity he realized that this is the very language with which to describe the very structure of the space and time of the Universe itself! It would be hard to conceive of something more real than that.

   [Einstein was himself not so familiar with this branch of mathematics, and recruited assistance for this from among his colleagues (contrary to popular belief, he was not 'bad at math', however, he had received poor math grades in school)].

   For books on this subject for the man on the street - multitudes have been written - almost any public library will likely have at least a few books on this exact topic in particular, probably under Dewey Decimal codes 500,521, and 539.