a cut across the grain of the fabric. This cut creates a garment that follows the curve of a woman's body. Very popular cut for evening gowns in the 1930's and 1940's.

cutting fabric diagonally across the grain, causing the material to drape fluidly and elegantly across the body. Expensive due to it's inefficient use of fabric. Often used for silk or satin dresses for maximum slink factor. Popular in the 20's and 30's and now a dress signature of amongst others John Galliano. examples

If you look closely at most fabrics, you can see they are woven on a grid pattern (the warp and weft). Fabric is usually cut straight across these vertical or horizontal lines. A cut is made on the bias when it is made at a diagonal to the warp and weft. Typically, fabric cut on the bias moves and drapes very well.