Unlike other painting mediums which are classified by what the pigment is suspended in (e.g., acrylic, oil), tempera paints are defined by the surface it dries to become. Tempura paints dry to a hard, sandy, almost rocklike finish.
Traditionally, tempera paints were created by mixing a salve (something that dries hard and chalky) made of egg whites with pigments (usually ground flowers or insects).
Today, tempera paints can be made in larger quantities than before since the chemical compounds used to create them are more abundant than ground wildlife and egg whites. High-quality tempura paints today are created from pigments derived from minerals and salve made of slow-drying compounds such as talc and gypsum.
Often referred to as "poster paint," student's tempera are a less-expensive alternative. They are created by mixing cheaper pigments with an adhesive mixture much like wood glue.
If you'd like to try to create your own tempera paint, it's really not hard. Mix any powdered pigment (you can find some at your local art store) with an adhesive mixture that includes wood glue. This is one way to overcome the fact that commercial tempera paints come in a very limited selection of colors.