response 3 of 3:

Sep 6 16:05 UTC 2007

This seems a clear explication:
http://www.physlink.com/Education/AskExperts/ae168.cfm
"Tensors, defined mathematically, are simply arrays of numbers, or
functions, that transform according to certain rules under a change of
coordinates."

It may be possible to tailor a more revealing answer if you describe the
context in which you wish to understand tensors.

Some work is being done comparing the mental and physical "worlds" using
tensor calculus. There is an apparent contradiction between (mental,
propositional) logic and observable, empirical "reality" (quantum
logic). Tensor calculus can be used to specify and analyze the
discrepancies with an eye toward reconciliation.

I'm no mathematician, but perhaps I understand that tensor calculus is
used to analyze neural networks.
(http://plato.stanford.edu/entries/connectionism/ and
http://plato.stanford.edu/entries/language-thought/)

Perhaps you haven't read the links to 'tensor' in the Stanford
Encyclopedia of Philosophy:
http://plato.stanford.edu/search/searcher.py?query=tensor

Especially the The Foulis-Randall Example:
http://plato.stanford.edu/entries/qt-quantlog/