Ah, emacs. My favorite editor. Emacs is an extensible editor, with its (present) extention language being a dialect of LISP. In the beginning, it was TECO. At least one emacs clone uses C (or a C like language) as an extention language.
Emacs is not a moded editor, at least not in the sense that vi is moded. Most commands are written in the extention language. Some files of interpreted or compiled commands are always loaded on start up, some can be loaded via a ``run commands'' initialisation file, and some are loaded under direct or indirect user control. Commands can be bound to certain key sequences, and there are a number of defaults present for things like moving the cursor, deleting text, etc. Commands that are not bound to keys, can be accessed via the Meta-X (often Escape-X) command: which pops up a mini command line at the bottom of your editor screen. Emacs has command completion, if you hit the tab key and emacs can figure out the rest of the typing, it will complete the typing for you.
While vi will allow you to get a shell escape, emacs will actually run a shell inside the editor in a special ``process'' window. Back before windows, it was often safer to debug programs running them inside an emacs clone than it was to run them from command.com.
While emacs is not a moded editor, it does have modes of operation. On my SuSE 5.3 Linux installation, running (GNU) emacs with no arguments (files to open), you will get you a ``scratch'' buffer in ``Lisp Interaction'' mode. This mode displays to you a small introduction (or help) screen pointing out how to get out of emacs, mentioning something about file recovery, and mentioning that a tutorial is available (and some other things). There is a lot of online documentation for emacs. Most of this is either provided along with the commands that are loaded, or in the info system. The top level info page on emacs (info emacs) is almost 700 lines long on my machine.
Running a special help command (apropos) on the word ``mode'', I bring up a 686 line file of commands that have the word mode in them. Many of these modes are (computer) language specific: LaTeX, TeX, ada, ams-tex, archive, asm, awk, bibtex, C++, C, CWebm DCL, DSSSL, Emacs-LISP, F90, FORTRAN, HTML, Icon, IDL, java, LISP, M4, Maple, Metafont, MetaPost, Modula-2, nroff, Objective C, Pascal, perl, Prolog, Scheme, Scribe, SGML, Simula, Slitex, TCL, VHDL, Web and XML. Other modes allow emacs to emulate various kinds of vi editors, and even WordStar. There are modes for reading (or composing) mail, for NetNews, for surfing the web. And a host of other things.
One mode I was recently introduced to is emacspeak, a mode whereby anything under control of emacs can have screens, lines, words or characters sent to a speech synthesizer so that visually impaired people can operate a little more efficiently. A great deal of the power of emacspeak is due to the fact that it is so powerful, and has some many special functions available.
Just on a lark, I thought I might look to see if http://www.emacs.org/ existed, and it does! It looks to be in a major overhaul right now (for instance, the elisp archive is unavailable), but this should be the place to go for up to date information on what's happening with the world's most complicated/advanced editor.