What's a working shawl?  It's a large shawl you use as a prop, not one you wear around your shoulders.  Some shawls are easier to work with than others, and your needs will change as you become more skilful.

Non-flamenco dancers may have seen men twirling and flicking a cape in dances like the paso doble:

Whether the shawl dances are derived from the bullfighting cape is a matter of debate - but the important thing is, a shawl can be a spectacular addition to your repertoire.  In the next two clips, you can see the difference between the smaller, lighter shawls used by amateurs and the huge, heavy professional shawl:

For advice on how to choose a shawl, see Choosing a Flamenco Shawl.