Codex
Codex comes from the Latin word for "book." If you want a book to sound really fancy, render its title in faux-Latin and stick the word "Codex" in front, like "Codex: Canus Latinicus."
In Warhammer 40,000
Since the Second Edition of Warhammer 40,000, each army book and expansion published by Games Workshop has been titled "Codex: Insertfactionhere." The term "Codex creep" refers to the fact that the Codices currently in play have been published across three editions and ten years, and it seems that the latest Codices (especially the half-dozen flavors of Space Marines) are more powerful than the older ones in order to entice people to buy the army of the month.
Sometimes the different classes of codices and expansions are nicknamed with some descriptive term ending in "-dex" (cf. the different flavors of Carnifex nicknamed with something ending in "-fex"), like the "mini-dex" books from Third Edition that contained special rules and a few extra units for an army list that has been published already (e.g. Craftworld Eldar as an expansion for Eldar, or Catachans as an expansion for Imperial Guard).
The word Codex is also used in the universe of Warhammer 40,000, like the Codex Astartes.
It should be noted that the Codex release and update schedule is of great concern to the 40k fanbase, and thus all of /tg/. Once the slightest hint of a new codex being released is given to one, sweaty neckbeard, all of the internet knows about it by days end. Once such an inkling is heard, rumors of the new Codex being overpowered, pandering to the latest edition's new features, screwing the owning faction's canon over, laying a plague upon our crops, and draining the light from the sun itself abound with fervor and gusto, dividing the community, and especially the specific faction's playerbase, into a veritable rage-rainbow of skubdivisions.
The especially hot-button issue in the inevitable debate once the shadow of an unannounced new Codex looms is who the writer will be. In the eyes of many players and fans, this and this alone will determine if the Codex will be "bad" or "good", fun and balanced or overpowered and min-maxy. With the rise of Matt Ward (say what you will about him, the man churns out books at a Stephen King-esque rate (well at least before the the poor bastard got blindsided by a goddamn minivan)) and a strange dip in the variety of GW Codex writers, there is now an inevitable list of writers that every Codex will have attached to it, before the real writer is announced.
The Inevitable List will Always Include: Matt Ward, Phil Kelly, Aaron Dembski-Bowden, Dan Abnett, Joss Whedon, Stephenie Meyer, Philip Reeve, Scott Westerfeld, Terry Pratchett, George Lucas, Neil Stephenson, Neil Gaiman, Sheldon Cooper, J.K. Rowling, J.R.R Tolkien, M. Night Shamalan, The Doctor, Kermit the Frog, Moira Brown, Bilbo Baggins, Nigella Lawson, Frankie Boyle, James Patterson, Stephen King, Anonymous, Aristotle, Sauron, Shakespeare, Plato, God, Satan, and Egoraptor.
Of another concern is the slowly rising prices of the codexes, especially in recent years. Where as several years ago they were at most £12 for the average book, most recently the cost is going up to £35 pounds, a massive leap and a bigger dent in the pocket before you even buy miniatures. This is particularly important to space marine players, considering how often their army gets redone, they will be buying a new expensive codex every couple of years at this rate.
Supplements
A supplement is a mini-codex, an add-on containing additional rules in order to have an army from a mainstead codex with unique features and abilities. This is as awesome in theory as it sounds but the supplements of recent years have suffered in varying levels of quality up and down like a roller coaster.
The peak of supplements was back in the early 2000, back in the 3rd Edition when you could get supplements like Codex Craftworld Eldar; Catachan; and Assassins. For a small cost of £4 you could get a bunch of rules allowing you to customise your army, some quality fluff and a scenario or two. It was short, neatly packed and exactly the worth of price you were paying.
Since that time thought GW has gone down the dark route of profit mining and the supplements are no exception to what has happened in recent years. Supplements are no longer the small extras from before but now the same size (and cost) as the mainstead codexes, While this may not sound like a problem you still have to have the main ones in order to use them and depending on the writer current edition supplements can be hit or miss. Black Legion is considered perfectly acceptable for example while Iyaden and Sentinels have received their fair share of problems.
Some supplements such as Blood Angels, Dark Angels, and Space Wolves from the 3rd have swung full on army and mainstead codex releases now. To allow you to use their rules beyond their specific chapters the fluff on their seconding founding chapters have been expanded (which at least is a good silver lining).
In Warhammer Fantasy Battle
The army list books and expansions for Warhammer Fantasy Battle are called Army Books for no actual reason, so many 40k players who are also WFB players just call them Codices. Funny how the Sci-Fi setting has the old fashioned term and Fantasy the more modern term.
Similar to the issue facing 40k-ists, the price of the Warhammer army books has risen sharply in recent years. From a price of £10 the most recent books are now £30. Thankfully fantasy armies are not redone as often as space marines in 40k although The Empire, Orcs and Goblins and Chaos should be worried until they see an update on the horizon...