If you're not a gearhead, listening to car people talk can be really puzzling. You could easily eavesdrop on a couple of gearheads and hear them talking about how they're going to drop the Celebrity's tranny so they can pull the head off the Iron Duke*. And none of that statement is illegal.
But even us gearheads occasionally realize that we have no idea what words we've been hearing for years actually mean. Let's start with the word "brougham."
"Brougham" has been used as a model name on a ton of (mostly) American cars from the '70s and '80s. Look at this partial list of cars that used it from Wikipedia:
Cadillac Fleetwood Brougham
Cadillac Eldorado Brougham
Cadillac Sixty Special Brougham
Oldsmobile Ninety-Eight Regency Brougham
Oldsmobile Cutlass Supreme Brougham
Pontiac Parisienne Brougham
Pontiac Bonneville Brougham
Chevrolet Caprice Classic Brougham
Ford LTD Brougham
Ford Torino Brougham
Mercury Marquis Brougham
Chrysler New Yorker Brougham
Dodge Monaco Brougham
Plymouth Valiant Brougham
AMC Ambassador Brougham
That's a lot of Broughams. Usually, the term was used to differentiate the most opulently luxurious member of a given model. Back in the 70s, that often meant opera windows, as much of the upper half of the exterior covered in vinyl as possible, and an interior that would even make a Victorian prostitute suggest that maybe you could dial back the tufting and quilting a bit.
Okay. So what the hell is a Brougham? Well, the name comes from the Right Honorable Henry Brougham, 1st Baron Brougham and Vaux. Old Henry B (1st Baron B&V) was statesman and jurist, but I think the coolest-sounding thing he did was to found something called the Society for the Diffusion of Useful Knowledge. Oh, and there was also a carriage invented for him.
This carriage is the real origin of the Brougham (pronounced 'broom') term in the automotive context. The carriage was a four-wheeled vehicle, with the rear half enclosed and containing at least one bench seat for, normally, two. Sometimes there were jump seats. It had a forward-facing window, which separated it from a regular coach. The driver and footman sat on the forward exposed seat, getting cold and rained on because they didn't have enough sense to be born into a wealthier family.
Later, an automotive body design came around, and was named Brougham after the carriage. The body style was similar to a Town Car, with passengers enclosed and cozy and the help stuck outside, in the elements. They seem to be a bit smaller than Town Cars tended to be.