A softbox is a box that fits over a flash head or tungsten lamp made of black sides, with white, gold or silver interior and a translucent front where light passes through. A softbox is most popular for it's soft, even light. Softboxes are used heavily in portrait photography and many other types of commercial photography.
The light that comes from a softbox is directional and diffused making it a light that is easy to control. The Softbox eliminates hot spots and evenly distributes the light as well (see photos below). Accesory grids can be attached to the front of the softbox to keep light from spilling onto unwanted areas of the scene.
Photos courtesy of Photoflex.com
Softboxes come in various sizes for different lighting circumstances. The larger the light source is relative to the subject, the softer the light will be. In addition, the closer a softbox is to the subject, the softer the light will be. For this reason, small softboxes are typically used for small object photography or for dramatic lighting of larger objects. Larger softboxes are most often used for people photography.
Softboxes can usually collapse for easy storage or transport.