These are sometimes referred to as yoga or athletic headbands. Unlike other headbands they have thin rubber strips on the inside to keep them from slipping. Those rubber stripes are what make them so useful for braiding. They can be used when working with especially slippery fibers, off-balanced braids or when making beads as fiber braids (CBB).
It is important to get the wider headbands, about 1.25 in. (3.125 cm), as they have four rubberized stripes on the inside.  They usually come in a pack of two, and you will need both of them. One will be placed around the outside of the marudai mirror with the rubberized side up against the wood of the mirror. The second one goes on top of the first with the rubber stripes facing to the outside.

Important Note: If you have my DVD, then this will be something new. At that time I was using the rug pad as Jacqui Carey suggested.

Where to buy the headbands: Walgreens, CVS and other similar stores as well as Walmart. I was also able to buy some of them online.

An Alternative Option:
In Jacqui Carey’s book, The Book of Braids, she tackled the problem of off balance braids by placing a rug pad on top of the marudai mirror. Although, I think that the headbands work better, if you can’t find the headbands or have some of this on hand it will also work.