Artifacts are super-nifty magical items that usually do more than one thing. They can be obtained by characters who complete certain quests. On the whole, most artifacts can be replicated in an Item-Maker, although some serious side-effects are usually required to balance out the powers. Some artifacts (the Oghma Infinium, for example) cannot be replicated.
There are two general types of artifacts available in the game: aligned and non-aligned. Aligned artifacts are obtained through the process of summoning a Daedra Prince and completing the required quest. Non-aligned artifacts can only be obtained through Knights Guild quests (available only to members of the guild). It has been said that a player can only have one artifact at a time. This is completely false. A player can have as many artifacts as he/she can gather.
Most artifacts allegedly disappear after a year and a day, but it has been my experience that they simply wear out, the same as any other magical item. However, like any other magical item, they can be repaired by an item with the "Repair" power.