Precious resources consist of Crystals, Gems, Mercury, and Sulfur. They are rare in the sense that their mines are not ever-flowing on the map. Each mine will produce one precious resource per day.
Precious resources are often used to purchase the high-tier creatures and their upgrades.
Heroes III introduces artifacts that increase your income of one of these precious resources each day, further aiding your supply, as they are most used also in the building of the Mages Guild.
In Heroes VII, the precious resources are replaced by Dragonblood crystal, Shadowsteel, Starsilver, and Dragonsteel.