There are several variations of this bind-off. The most well-known is from Elizabeth Zimmermann’s Knitting without Tears.
Benefits and Drawbacks
This bind-off creates a very stretchy edge, suitable for neckline and sock-top edges.
Using a tapestry needle with an extremely long tail of yarn, pull the needle through two front loops as if to purl, then back through the first stitch as if to knit. Drop the first stitch off. Repeat to the end.
Pull the yarn tail through two front loops as if to purl, then back through the first stitch as if to knit. Move the first stitch to the right-hand needle, making it the last stitch of the round. Follow traditional method as above.
See Binding Off for links to more stretchy bind-offs.