Materials are the wide array of base items needed to create objects. Different materials have different base value multipliers which can make otherwise identical items worth considerably more or less. A gold throne is worth more than an identical quality copper throne, and so on.
Not every end-product can be made of all materials. For instance, obsidian is the only stone that can be used to make weapons. While nearly all metals can be made into furniture and crafts, only a few can be made into weapons and armor. This (alone) doesn't necessarily give these materials a higher base value, but it may make them worth more to you and your fortress in a practical sense.
Some dwarves have preferences for one material over another - they tend to produce higher quality items if they are working with that material, and perceive items (or rooms) made of that material as higher quality, which can give them happy thoughts.
General groups of materials include, but are not limited to,
Certain materials tend to be geared toward making certain items. While stones, wood, metal, and glass can be made into similar furniture, there are some items which are normally restricted to certain materials. For example, beds can only be made out of wood, and bins, barrels, and buckets cannot be made out of stone or glass. Cloth and leather can both be made into clothing, but leather can also be used to make armor. Gems are largely for encrusting finished items made from other materials. Of the dozen different metals, only half are usable to make weapons.
In all cases, each group of material is divided into many possible sub-types of material; there are, for instance, 7 pure metals, another 4 alloys from those, 23 types of stone of which 6 are of special value, and 18 different types of gems organized into 4 groups according to rarity. It is best to look up each individual category or material to become familiar with its value, and what it can and cannot be used for.