It is thought the name is derived from Biscay, as in Bay of Biscay, but the crustaceans are certainly bis cuites "twice cooked" (by analogy to a biscuit) for they are first sautéed lightly in their shells, then simmered in wine and aromatic ingredients, before being strained, followed by the addition of cream.
Bisque is a method of extracting flavor from imperfect crustaceans not good enough to send to market. In an authentic bisque, the shells are ground to a fine paste and added to thicken the soup. Julia Child even remarked, "Do not wash anything off until the soup is done because you will be using the same utensils repeatedly and you don't want any marvelous tidbits of flavor losing themselves down the drain." Bisques are thickened with rice, which can either be strained out, leaving behind the starch, or pureed during the final stages.
Seafood bisque is traditionally served in a low two-handled cup on a saucer or in a mug.
Bisque is also commonly used to refer to cream-based soups that do not contain seafood, in which the sometimes pre-cooked ingredients are pureed or processed in a food processor or a food mill. Common varieties include squash, tomato, mushroom, and red pepper.