PDF is an Acronym and FileExtension for Portable Document Format.
PDF is a format specified by Adobe which describes how to embed a multitude of resources in a single file, and also defines and describes formats for these resources, primarily PostScript with extension functions to enable the features PDF delivers beyond PostScript. Essentially, it is not a descendant of PostScript so much as an advanced container format for PostScript documents.
PostScript (and the Type1 font format, for that matter) are, of course, also Adobe brainchildren.
PDF is the format of choice for distributing documents because:
The obvious way is Adobe's commercial AdobeAcrobat, and if you're a professional and need all of the advanced features of PDF, that is your best bet. If you are less ambitious, there are many other, completely sufficient options available; see our CreatingPDFs page.