Portable Document Format (PDF) is Adobe's follow-on to PostScript, defining a true document technology. PDF defines the full architecture of a document, in all its pages and content. The author of the PDF defines exactly how the document should look, including having a table of contents and index which reference absolute page numbers. The result is a "final form document", with no inherent editability. The author may go further, and cause instructions to be embedded in the PDF which prevents its printing.
Modern printers, which can process PostScript 3, usually also have an interpeter which can handle PDF directly. Thus, you don't have to first generate PostScript from the PDF in order to print.
PDF rigidly defines the document, which has a fixed layout. This means that the document looks exactly how the author intended, but also leaves the document non-adaptive. In a PDF, a page is always a page: if you look at a PDF on a Web page, you see all these fixed-width text lines and page breaks rather than a continuum of text flow as you get with HTML text. Further, the content of a PDF is static, where PDF was designed for printed output.
The rigidity of PDF is in stark contrast to the flexibility of eReader technologies, where content can adapt to the device viewing it, and to the requirements of the reader. Open an eBook on an iPad: you can view a single page in portrait, turn the iPad 90 degrees to see two pages at once in landscape (with the amount of text on the page changing); and you can change the font and its size to make your reading easier. Further, with Apple's iBooks technology you can have interactive content, with music, narration, movies, rotatable images, etc. This is way beyond PDF.
Adobe's PDF technology allows you to do an awful lot with a PDF. You can sign it; you can protect it; you can annotate it; you can change the order of pages; you can fill in some PDFs. Where the text content of a document is digital (rather than image), you can search for words, and click from the table of contents or index to immediately go to content.
On the Macintosh, the provided Preview application allows you to do all kinds of annotation of PDFs, plus removal and re-ordering of pages. (Preview has always been way faster than Adobe Acrobat Reader.) Various apps are available for the iPad for annotation.
Tip: Did you know that U.S. tax form 1040 PDFs and its kin are fillable forms? You can fill in fields and checkboxes on your computer rather than dealing with paper and hand writing. Other online sources of forms may also provide them as fillable: try them. You can create your own fillable forms using appropriate software, such as Adobe sells (Acrobat).