A garment is said to be cut on the bias when the fabric's warp and weft threads are at 45 degrees to its major seam lines; essentially, the diagonal cut of a fabric. This technique utilizes a greater stretch in the bias, thereby causing it to accentuate body lines and curves and drape softly. Non-woven fabrics such as felt do not have a bias. Bias-cut garments were made popular by French designer Madeleine Vionnet in the '20s and '30s.
To see some cute bias-cut items, read more.