For most Americans this really is a mouthful. Is it 'War-chest-ur-sheer'? 'Worst-er-shur'? 'Wur-sest-ur-shy-er'?
The name of the UK county of Worcestershire is pronounced 'woost-er-shy-er'. The sauce is therefore pronounced the same, or is often simply known as 'Worcester' ('woos-tah') sauce.
Now what exactly is in that mysterious dark liquid, where did it come from and what do you do with it?
According to Wikipedia:
Worcestershire sauce is a widely used fermented liquid condiment manufactured by Lea and Perrins, in Midland Road, Worcester. The genuine product, manufactured to the original recipe, available in the U.K., comprises malt vinegar (from barley), spirit vinegar, molasses, sugar, salt, anchovies, tamarind extract (the not-so-secret "secret" ingredient), onions, garlic, spices, and flavouring. It is a flavouring used in many dishes, both cooked and uncooked, and particularly with beef.
Legend has it that a British nobleman, on returning from India in the 1800s, requested some local Worcester chemists (Messrs. Lea and Perrins) to develop a curry powder for him. The chemists then realized that their concoction would make a nice sauce... The veracity of this story is, however, likely lost to history and Lea and Perrins' sauce is now the stuff of urban legend, including tales of sorcery, ghosts and seismic resistance.
It's possible to make your own sauce at home, but to be honest I don't think it would be worth the bother. Keep a bottle on hand to throw into caesar salads, bloody mary's, shepherd's pie and even some Indian recipes! When I was growing up, our kitchen was never without a bottle...