Anchovies are any one of many species of small, silvery fish of the Engraulidae family which live in all the world's oceans. They move in huge schools in much the same way as sardines do. In fact, anchovies are often confused with sardines, but the former can be distinguished by their larger eyes and mouths. Anchovies feed on plankton and fish larvae and are eaten in turn by seabirds, marine mammals and many species of fish, including rockfish, tuna, shark and salmon. Such is the food chain of life.
Though anchovies are fished in Asia, the Americas and Europe, western gastronomes assert that the only "true" anchovies come from the Mediterranean area (Engraulis encrasicholus, don't you know). If you don't live in southern Europe, you won't often find fresh anchovies, which is too bad, because they are delicious, if rather bony, when fried or grilled. Think of what you'd do with a fresh herring or sardine, and do it with your fresh anchovy. Yummy.
More usually, however, at least for those of us who don't live around the Mediterranean, anchovies are sold fileted, cured in salt, and canned in oil; they may be laid flat or rolled up in their tins. Anchovies are salty anyway, but cured like this they're really salty (about 20% salt), so rinse them in cool water, or even soak them for half an hour, drain, and pat them dry before using.
You can also buy tubes of anchovy paste, which you can't rinse but which is convenient to use and easier to store than leftover anchovies (which you need to remove from their tin and store in the fridge covered in oil; they'll keep for a month or two.) Half a teaspoon (2.5 ml) anchovy paste equals 2 anchovy filets.
Because of their strong flavour, anchovies are usually used as a seasoning rather than the star of your meal. They are an integral ingredient in real Caesar salad dressing (not that weird creamy stuff in a bottle) and make an exciting addition to pizza or pasta.
So what about all those anchovies that are caught in other parts of the world? Asians, of course, don't care what western gastronomes think, and eat theirs or use them to make fish sauce, but the anchovy fishery in the Americas primarily yields fish oil, fish meal, and bait.