Hypertext is the means by which hyperdocuments are created, a hyperdocument being a set of pieces of information among which the user can "jump" by following hyperlinks. Contrast a hyperdocument with a printed book, which forces the reader to go through it in page sequence. Hypertext contains not only human-readable information, but metadata about how that information is to be organized and presented.
One might argue that it is possible to go to the index or table of contents of a book, and then jump to a topic of interest, but a hypertext architect would explain that the index or table of contents is actually a list of links. Going from opening the book, to going to the table of contents, and then turning to a page is analogous to clicking a hyperlink and going to the page of interest.
At present, the most common hypertext notation is the Hypertext Markup Language (HTML), maintained by the W3C Consortium. The most common implementation of hypertext is in the World Wide Web, although it is quite common to have information on removable media (e.g.,optical disk) written in HTML.
Ted Nelson is generally credited with first mentioning the term "hypertext" in 1963, at Project Xanadu.  The first published reference to it appears to be in a college newspaper article about a 1965 lecture he gave in 1965, entitled ""Computers, Creativity, and the Nature of the Written Word" 
The first commercial implementation of computer-based hypertext was Hypercard, a software package for the Apple Macintosh developed by Bill Atkinson and first shipped in 1987. It was possible to transfer complete hypertext files between computers, but the fundamental idea of the World Wide Web, with parts of hyperdocuments spread across multiple computers such that links can be followed in real time, came from Tim Berners-Lee in 1989.
Berners-Lee first intended his concept for internal use at CERN, the European high energy physics research later. While the broadening of that concept into the Web is beyond the scope of this article, the idea of hypertext is much older than the Web. It was the genius of Berners-Lee to spread the hypertext worldwide, and of Marc Andreessen to develop and distribute the first user-friendly web browser.
Various markup languages intended to give typesetters and printers information on choosing fonts, aligning text, etc., are the totally manual antecedents of hypertext, in that they give metadata on organizing information, beyond the information itself. PostScript is an early automated version of a printer description language.
While it is possible to write directly in HTML, the usual practice is to use various authoring software, based on a what you see is what you get WYSIWYG model. The author simply creates a table such that it looks the way the author wants it to look, and the software will translate that visual construct to HTML. HTML is not easily human-readable.
- Home Page of Ted Nelson
- Nelson, Ted (1965), "Ted Nelson Discovers Hypertext", Living Internet
- Berners-Lee, Tim (March 1989), Tim Berners-Lee's proposal: "Information Management: a Proposal"