In the 1970s, the famous American mathematician and computer scientist Donald E. Knuth started writing TeX, a computer program which could (semi)automatically typeset his seminal work “The Art of Computer Programming”. TeX became a Turing-complete (though rather low-level) programming language, enabling building higher level languages on top of it (a bit like LISP).
One of such languages is LaTeX, whose development started in mid-eighties by Leslie Lamport. About a decade later, LaTeX2e (pronounced LaTeX-two-epsilon) was delivered, now by the newly formed “LaTeX team”; this is the “current version” of LaTeX.
Meanwhile, many people wrote various add-ons (called “classes” and “packages”), which are now counted in thousands, and add various features to the core LaTeX. (They cover a wild range of uses, from typesetting bibliographies to adding hyperlinks to the documents to presentations to chemical notation to putting together images of chess boards.)
Currently (as of 2012), much work is done on the “LaTeX3 Project”, whose parts are already usable as LaTeX2e packages (think Python’s import future
).