Simply put, to knit on the bias is to knit diagonally, rather than straight up and down or side to side. Interesting style lines and drape can be accomplished by knitting on the bias, as well as distributing color differently if you are using a space-dyed yarn. The eye is often amused to see a traditional texture set at a slant. The torso and front of the Elfin Goth is all knit on the bias.
When knitting on the bias, there are a few ways to approach it. It is a question of where you plan to place the increases and the decreases. If you plan a symmetrical garment (like the Elfin Goth) , you will want to place the increases at the side seams and their matching decreases at the center seams or vice versa, so the fabric will slant to each side with a V or upside-down V at the center seams. If the item will be asymmetric, put the increases at one edge, and the matching decreases at the opposite edge to make the fabric slant to one side.