One can reasonably say that PDFTeX is (today) the main stream of TeX distributions: most LaTeX and many CONTeXT users nowadays use PDFTeX whether they know it or not (more precisely, they use PDFTeX extended by e-TeX). So what is PDFTeX?
PDFTeX is a development of TeX that is capable of generating typeset PDF output in place of DVI. PDFTeX has other capabilities, most notably in the area of fine typographic detail (for example, its support for optimising line breaks), but its greatest impact to date has been in the area of PDF output.
PDFTeX started as a topic for Hàn Thế Thành’s Master’s thesis, and seems first to have been published in TUGboat 18(4), in 1997 (though it was certainly discussed at the TUG’96 conference in Russia).
While the world was making good use of “pre-releases” of PDFTeX, Thành used it as a test-bed for the micro-typography which was the prime subject of his Ph.D. research. Since Thành was finally awarded his Ph.D., day-to-day maintenance and development of PDFTeX 1.0 (and later) has been in the hands of a group of PDFTeX maintainers (which includes Thành); the group has managed to maintain a stable platform for general use.
Development of PDFTeX has mostly stopped (only bug fixes, and occasional small development items are processed): future development is focused on LuaTeX.
This answer last edited: 2011-05-28