Minerals are naturally occurring, inorganic, crystalline solids with a narrowly-defined chemical composition. For example, quartz -- silicon dioxide or silica -- has the chemical formula SiO2 wherever on Earth (or off-Earth for that matter) it is found. Pure calcite is always CaCO3. Malachite, a beautiful green copper ore, is always Cu2(CO3)(OH)2.
Rocks, on the other hand, are made (mostly) of minerals as, say, a loaf of bread is made up of flour, yeast, liquid, and other ingredients. Granite, which primarily consists of the minerals feldspar, mica, and quartz, is a rock. Usually rocks contain two or more minerals, but not always. Sandstone, a sedimentary rock, could consist entirely of grains of quartz that have been cemented together, though it may also contain feldspar or any number of other minerals.
Rocks may also contain non-minerals. Obsidian, a volcanic glass, is not considered a mineral because its structure is amorphous rather than crystalline. Jet, a relatively hard form of coal that can be carved, is mostly carbon from ancient plants, and thus is by definition a rock not made of minerals.
*Much of the information in this article comes from Rocks and Minerals: A Guide to Field Identification.
The terms "rocks" and "minerals" are often linked, and are nearly as often confused with each other. The difference between the two is easy to learn, though identifying them is harder!