Despite its name, this is really a very innocuous piece of yarn-lover equipment. It is no more and no less than a small mesh pouch. A center pull ball is placed within the yarn bra, so the yarn can feed out through the opening. The yarn bra holds the outside end of the yarn in place, and generally keeps the ball from unraveling from the outside. This is useful in both use and storage, and depending on what you use for a yarn bra it can also keep your yarn clean.
A yarn bra can be knit, crocheted, macramed, woven, or sewn. But, why bother? The mesh bag off of a 3-pack of garlic works just as well. I've met a woman who uses the foam packing that sometimes comes on asian pears and other delicate fruit. Of course, knitting or crocheting little pouches for your yarn is a good way to use up odd-balls, and looks quite a bit nicer.
Disclaimer:
I don't use yarn bras. I use Ziploc bags if necessary, but rarely keep yarn of the same color and variety separated. On the other hand, I often have to rewind the last 10 yards of a ball.
If you are looking for a pattern for a knitted bra, try Lily Chin's book The Urban Knitter. It has one which looks pretty good, although I haven't tried making it myself. Thanks for the nudge m_turner.