Made popular by Madeleine Vionnet, this cut revolutionized fashion in the 1920s and 30s. By cutting fabric against the grain at a 45 degree angle, the bias cut effectively allows the fabric to fully stretch.
The greatest benefit of this cut is that designers can choose which body parts (usually the curvy areas) to accentuate while maintaining a soft feminine drape to the fabric.
This Betsey Johnson Dress is a fabulous example. (And not terribly expensive for a Betsey Johnson dress at $99 on ebay, size 6)
Item number: 190121217595
And for those of us with less cash to burn, I found this cute skirt for $50.