Function is the obvious. What's this item for?

Equipment is something you wear. A sword. A piece of armor. Duh, no brainer here. Equipment says exactly what inventory slot it is used in, and any aspect of the text written in red means that you can't use it for that reason. (Mail would be in red for a druid, level 35 would in red to a level 30 character.) Equipment is the only type of item that quality truly applies to, although tradeskill items sometimes have one.

Consumables are items you use. Food and drink. Potions. Scrolls of stamina. You right-click them in your bag, they do something, and they disappear. (Arguably, ammunition could be consumable, but that isn't how you use it.)
 
Quest items are objects you acquire, usually but not necessarily from corpses, that specifically say on them "quest item", and are for the explicit purpose of completing a quest. You will usually not see a quest item unless you actually have the quest. Some items for quests are not marked as "quest item"s, which means they have an additional purpose. True quest items do nothing else, and cannot be sold to vendor.

Junk items, sometimes called vendor trash, is anything that does not fall into one of the preceding categories, and when you mouse over it, its name appears in GRAY LETTERS. Anything that meets this criteria is only meant to be sold for money when you get back to town.

Tradeskill items are anything that doesn't have an obvious purpose, but has a name in usually white letters, or sometimes one of the higher-quality colors. It may not be obvious what exactly, but it will be used in *some* tradeskill recipe. Obviously herbs, ore, and leather fall into this category. Tradeskill items often make a decent sum of money in the auction house, but if you can't figure out what it's good for or don't feel like wasting the time, it might be worthwhile just to sell the item anyway. (Chances are there aren't too many people looking for Zesty Clam Meat anyway.)

And there are a few miscellaneous items that don't fall into any category. Bags have a fairly obvious purpose. If you have a mount or a non-combat pet, you will possess an item that calls or summons it. (Nightsaber reins, bird cage, cat carrier, etc.) Skinning knives, fishing poles, and mining picks aren't really tradeskill items, nor do they do anything directly.

Additionally, most things you wear have an item quality, indicated by the color of their name. Most items you pick up initially will be gray, indicating the poorest of quality. White is one step up from this. Generally gray and white items have no properties to them other than just "armor 13" or "damage 5-8." Low-level quest rewards and very high-level whites are sometimes an exception. Green items and anything above that, for all intents and purposes, are magic items. They possess some additional benefit beyond protection or damage, usually a bonus to one of your attributes. Sometimes the bonus will be an effect, like an effect on a weapon that causes extra damage. Unlike white or gray items, these can be disenchanted. Blue items are much rarer than green. Usually greens only have one or two bonuses on them. Blue items often have three. All other things being equal, though, blue items have much lower required level than green for the effect. Blue items typically come as treasure from killing a boss in an instanced dungeon. Green items are sometimes randomly generated, a la the Diablo suffix system, but blue items are always the same. There are even higher qualities of item. Purple items are much more powerful than blue, and are extremely rare outside of loot from raid bosses. Beyond that is the almost non-existent orange category. Allegedly, some day, there may be red after this.

The item qualities do technically have names. Nobody uses them, and just refers to the color, which often makes item discussions sound like racial bigotry. If you want the "proper" terminology, gray is poor quality, white is common, green is uncommon, blue is rare, purple is epic, orange is legendary and presumably red will be artifact items. Of these, epic and legendary are the only names that get used consistently.

There is one other very important attribute to equipment - binding. An item that is soulbound belongs to you. Forever.