Postscript arrived as part of the Apple Laserwriter, a perfect companion to the Macintosh, the system largely responsible for the desktop publishing revolution of the 80s.

Postscript programs can be run to generate output on a pixel screen, a vector screen, a fax machine, or almost any sort of printer mechanism, without the original program needing to be changed. Postscript output will look the same on any Postscript device, at least within the limits of the device's capabilities. Before the creation of PDF, people exchanged complex documents online as Postscript files. The only reason this standard didn't "stick" was because Windows machines didn't usually include a Postscript previewer, so Adobe specified hyperlinks and compression for Postscript, called the result PDF, distributed previewers for it, and invented a market for their "distiller" tools (the functionality of which is also provided by ghostscript's ps2pdf and pdf2ps programs).

Postscript is a complete programming language; you can write software to do most anything in it. This is mostly useful for defining subroutines at the start of your program to reproduce complex things over and over throughout your document, like a logo or a big "DRAFT" in the background. But there's no reason you couldn't compute π in a Postscript program.

Postscript is fully specified in a publically available series of books (which you can find at any good bookstore) and also online at https://partners.adobe.com/asn/developer/technotes/postscript.html. Although Adobe invented it and provides the dominant commercial implementation, other vendors like Aladdin produce independently coded implementations as well.