TeX is a typesetting system released by Donald
E. Knuth in 1982; despite of its age, it is a virtually perfect and
bug-free piece of software. Some years later, following the indications
of some TeX users, LaTeX has been released; it is a set of macros which
made TeX more immediate less difficult to understand and use.
The main use of TeX (though nowadays LaTeX is
mainly adopted) is the processing of texts containing several
mathematical formulae; it is also used for documents of ancient
literature, archaeology, musicology (just to mention some examples).
The main difference with the most common word
processors is that LaTeX does not allow to modify the graphical look of
the document while typing, but the work is done with a pure ASCII text
that, according to a predefined syntax, is processed by TeX; the text
file is then converted to a DVI file and then viewed by a dedicated
program.
The main advantage of LaTeX is that you can focus
on the logical structure of the document, rather than on its
graphic look (which anyway shows itself to be excellent); it is then very
adviceable to use for scientific publications, Ph.D. thesis (not
necessarily in scientific or technological fields) and much more else.
Various implementations of TeX and LaTeX (the one that I am using and I strongly recommend is TeX Live) for
several operating systems (Win, Linux, Mac, etc.) can be downloaded from