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Tailoring is a skill that turns cloth (linen, wool, silk...) acquired from drops or from the AH (Auction House) into cloth armor, usually only useful for "clothies" (any class that cannot wair any armor better than cloth). This way, you can contantly improve your armor without having to wait for a good drop/reward. This goes hand in hand with enchanting or leatherworking. Leatherworking because some of the recipes call for leather, and enchanting because some of the armor you can make with tailoring is green or of a higher status than white, and can be disenchanted (no, disenchanting is not a separate skill, instead a enchanter disenchants things, gets thier magic components and uses those to enchant other things).

[edit] What you make

You can make cloth armor, bags, and bolts of cloth, which are needed by other professions to make certain objects. You cannot make weapons for obvious reasons (who ever heard of a cloth weapon???). Cloth armor really only sells to vendors or to you to wear in the beginning, but eventually you can sell the high green, blue, and purple stuff you make in the aution house for a huge profit (hopefully). Also, you can wear the armor you make yourself, which makes it useful to have a tailoring level until you can make stuff that require your level or higher to wear (other wise you will never wear the stuff you make because you already have better stuff) Everyone loves extra bag space, and tailorers are the only ones who can make them (I think), of course you can buy them for more at the AH or even (god-forbid) from a vendor, but why waste hard-earned money (I hate you all you Money buyers!) when you can make you own bags? The most basic recipes really only require the bolts you make from the cloth, and thread (which you buy from a vendor). The medium level recipes can call for things such as leather or spider silk (from drops from spiders obviously), and always call for more cloth/thread. The highest tailoring recipes call for a huge variety of material that you'll either have to run all over the world for (literally) or spend a fortune in the AH. However, the same holds true for all professions.