You forgot to mention how the artifacts are actually created.
For any object you pick up with the hand, e.g. rocks, fences, poo, etc. and put in one of your villages, the villagers will dance around these objects if they have nothing else to do, most likely in the evening times. It's a handy way to make use of the elderly who are otherwise useless from a productivity point of view.
Another fun bonus with artifacts is that they help increase a wonders size.
Let me explain.
The size of a Wonder (and hence the power of the bonus it gives you) is controlled by the amount of belief you have in that village. Artifacts help to add artificial belief. If you make about four or five artifacts, place them in a circle around the place you intend to drop the scaffold for the wonder. When you drop the scaffold in the middle of the circle, the size of the wonder you get will be MUCH bigger. Using this method, you can get major bonuses to your miracles, e.g. if you build a Norse wonder using this method, you will get over 50,000 wood with each casting of the wood miracle.
The catch is that because the wonder is bigger, it will cost more wood in the first place to construct, but it's well worth the effort. Once construction has started, you can still take your artifacts away and use them to impress other villages as Okapidragon described above.
If you use fewer artifacts in creating the wonder, you may not get the biggest one, but it still helps. The wonder scaffold just has to be placed near enough to the artifact for this to work.
Hope that helps.