These are types of pipes for smoking tobacco and both are associated with higher quality and cost, unlike say,other woods that all tend to impart their own flavors to the tobacco smoke and do not hold up to the heat as well. or clay, ceramic, corncob, gourd, plastic or metal each of which have drawbacks in performance tho all but the clay would be cheaper than a quality meerschaum or briar..
Meerschaum is a soft white mineral sometimes found floating on the Black Sea, and rather suggestive of sea-foam, hence the name, but the meerschaum used to make smoking pipes is mined.Watch as a miner brings the meerschaum up from a mine and an artisan carves an elaborate pipe bowl.
The briar for making smoking pipes is from the root burl of the tree heath (Erica arborea) a shrub or small evergreen. The 'perfect' probably refers to the lack of imperfections in the grain made by the polished method of making a briar wood pipe (there is also a sandblasted method) with preference given to the grain going straight up the barrel and not swirling or showing bald patches.
Watch this display of briar to get a glimpse of the craftmanship and art in the making of briar pipes.