To my surprise, there are various names used for a boom vang. Currently, boom vang is used in the US and kicking strap is used in the UK, but and older term is martingale. Basically, it is a pulley and/or a piston/rod systems that is used to level the boom and controls twist in the main sail.
Great, but when do you use it?
After searching around a bunch of books and web sites, I found a decent working description on the Sailing USA site:
If sailing close hauled or into the wind, the main sail doesn't really have twist. The boom vang is used in strong winds to flatten the sail and reduce the lift force of the sail. A flat sail can help avoid having to reef the main and will reduce excessive heeling.
p.s. If we had been smart like those folks on the Bella Star we might have found the corrosion under the boom vang plate and fixed it!