Sphagnum moss grows in large bogs, where it accumulates extremely slowly. Sphagnum moss is the living moss, and as it grows, layers of dead and decaying moss accumulate underneath. These decaying layers are called peat moss, the horticulturally valuable material. The usual method of harvesting involves ripping out large chunks of peat, which may have taken centuries to grow. Because of its slow rate of regrowth, many people feel that peat should not be considered a renewable resource.
Sphagnum peat of a high quality is produced in Canada. The industry in this country claims that "peat is accumulating nearly 60 times faster than the amount harvested" and that less than 0.02% of the peat bogs in Canada are used for harvesting. New Zealand also claims to practice sustainable peat production through harvesting methods that encourage fast regrowth. American peat is sometimes considered inferior and the bogs may not be as well managed, so consumers who are concerned about the environment, but still wish to purchase quality peat, are sometimes advised to use only Canadian products.
The decision about whether or not to use peat products is obviously a personal one. For further reading, see a critic's view here (scroll down to the first article under 2006) and the industry's defence here. If you decide not to use peat, coir dust, made from coconut fibres, is generally considered to be a high-quality replacement as a soil amendment, and it is becoming more easily available. If you are looking for something to replace those little peat pots, you can use coir pots, CowPots, a similar product made from manure, or make your own pots from newspaper, either by folding or using a potmaker.