From the Post Script reference manual:
"The Post Script(R) language is a simple interpretive programming language with powerful graphics capabilities. Its primary application is to describe the appearance of text, graphical shapes, and sampled images on printed or displayed pages. A program in this language can communicate a description of a document from a composition system to a printing system or control the appearance of text and graphics on a display. The description is high level and device independent."
Post Script is not just a file format. In fact, it is not a file format at all, it is a full-fledged programming language in every sense of the word; Don Lancaster has long been one of its most outspoken advocates.
EPS (Encapsulated Post Script) is a file format, sort of, but basically it is just a simple wrapper around Post Script programs that annotates simple things such as page boundaries.
Post Script the language was the basis of the Network Extensible Window System and Display Postscript.
Post Script is an explicit postfix-operator stack language, as is Forth Language, but they are otherwise unrelated
A while back I saw an example in a UK computer magazine of a Mandelbrot Set generator that was written in Post Script. You'd download it into the printer, and when it wasn't printing, it would generate the Mandelbrot fractal. Results could be retrieved via a bidirectional parallel cable.
A friend of mine was fond of doing this in the late 1980s. Adobe hired him, and eventually a large percentage of their in-house printers were running Mandelbrot (and later Pentaminoe-solvers) in their spare time.
Post Script is cool. I learned it from the books and used it to write a guitar tablature typesetter in PS some years back (www.ibiblio.org 
). It was written in PS to be Write Once Run Anywhere because at the time, at least with the university-based 'net community, you were more likely to have access to Ghost Script or a PS printer than any particular computer platform. Output is fairly poor by todays standards but someone wrote to me from NZ to say it had been used to typeset a book of banjo music...since it was written from the start to support any number of strings. After that, generating the EPS diagrams for my thesis was easy! -- Brian Ewins
See the newsgroup faq, www.faqs.org
Ghost Script is a free implementation of Post Script.
You can also find a front end for it called 'Ghost Gum'
See original on c2.com