As everyone else has said, "China." But, there's a bit more to it.
I'll leave you to your own reading of Buick's history on Wikipedia, but the modern brand basically emerged out of the destruction of Oldsmobile, Saturn, and Saab at GM during the last few years of the 2000's. Although Buick had a hell of a run throughout the '80s as a "fun" luxury brand with serious performance credentials, the shifts at GM throughout the '90s basically regulated them to the bargain end of the luxury segment. They weren't much more than tarted up Chevrolets or downgraded Oldsmobiles, and the people who bought them generally didn't care.
The death of Oldsmobile gave Buick a leg up in the luxury market, but only slightly, thanks to Cadillac getting the larger share of R&D and marketing bucks leading up to the bankruptcy in 2008/2009. Without a competitive powertrain, styling, and so on, they carried on with the W-body and L-body models that had largely been around forever at that point. Just before then, it was doctrine at GM that Cadillac was going to move further upmarket to actually compete with BMW and Mercedes (as we see today), while moving Saturn up to compete with Acura and Lexus - once again leaving Buick out in the wind when it came to R&D and marketing dollars. But, the weird thing was that the brand was selling like gangbusters in China, and someone at GM figured they could pass off Opels as Buicks elsewhere, and so they did - which also happened to be what was going on with Saturn in the US at the time. When Saturn got the axe, all of that cash went straight into the Buick pipeline, and boy oh boy did they rush into producing several cars that changed the game for them:
- Buick LaCrosse: After jumping off the W-Body onto the larger Epsilon platform, refinement seemed to go up a hundred fold. Although it is big/heavy compared to most of the Acura and Lexus competition, it does the soft/quiet/comfortable thing well enough to sell, and sell, and sell. Adding the standard hybrid mode didn't work all that well, but luxury AWD V6 did
- Buick Regal: A Regal to be taken seriously did great things for the company. They had a credible entry-level luxury car, even if most of the rest of the world loathe the Insignia that it shares the overwhelming majority of its parts with. The GS model sits in a weird performance zone that people seem to like, and even the lower trim level model attracts the kind of buyers that are looking for something that's quiet and stylish, without breaking the bank
- Buick Verano: More or less, Buick kinda lead the way with the foray into compact luxury cars here. Although Audi had done the A3 for a bit, it wasn't until Buick jumped in that the segment seemed to explode with options. Based on the Astra, again another car not well liked in all places, it shines with a pretty hefty bit of quiet-tuning and refinement that not all the rest of the luxury compacts have. That, and its a good bit cheaper than some of the competition
- Buick Encore: Welp. Buick hit the ball out of the goddamn park on this one. No one knew that the compact luxury crossover would become a "thing," hell, the idea of a compact crossover wasn't even a "thing" when this showed up. Cheap, good on gas, quiet, comfortable, and has optional AWD. They couldn't build them fast enough for quite a while, which was a similar thing to the...
- Buick Enclave: Although the full size luxury crossover had kinda/sorta been a thing for a bit here (I guess the Chrysler Pacifica?), Buick turned that segment pretty much upside down with the thing. I don't think anyone expected the Buick to be a volume seller on the Lambda chassis, and it still is all these years later. Again, comfortable, quiet, reasonably luxurious at a good price... It all adds up to a very successful formula at GM
Overall, Buick has been able to do a lot of things for GM that the other brands can't simply because there seems to be a lot less on the line. With the brand essentially limping into the 2010s, GM has largely figured that they can just pull the trigger on projects and see how they do - what more have they had to lose? As much as cars like the Verano, Regal and LaCrosse compete directly with the likes of the A3, TLX, and ES - they are likely to go into recently vacated territory with the Cascada this spring, and look to split their crossover business possibly in 2017 with a new mid-size unit. Just the same, the Avenir concept has been very well received, and it might be the first full-size, rear-drive Buick we've seen since the Roadmaster died in 1996.
TL;DR
Because China, and GM needs a brand to fill weird niche needs - which has so far paid off very, very well
That should be the real topic of this thread. Why does Lincoln still exist?
That's a much tougher question to answer than Buick. I think at Ford, its a lot of history with the brand, and I think its the marketing department.
As easily as they can charge $70k for a King Ranch F-150, marking up a Fusion to $40k+ levels isn't going to sit well with a lot of people when there is a blue oval on the front of the car. More or less, Lincoln serves as a logical step up for the Ford folks who will drive nothing but FoMoCo products. Although back in the '80s and '90s, there was also a clear distinction in the overall quality of the product as you went from Ford, to Mercury, to Lincoln... But without a Mercury to split the difference, and Ford largely moving up to fill that gap, there is little that they've been able to do to hide those similarities.
The even weirder part has been that the executives and the marketing department can't seem to make up their minds on what exactly is going on there. On the one hand, the execs are saying that they don't plan to go and chase down Cadillac and their German-fighting capabilities. On the other, the marketing folks are trumpeting Lincoln as the only true American luxury brand... More or less, that these are the comfortable, quiet, stylish cars that you'd expect to find... Not a hardcore Nurburgring monster that Cadillac has created.
Pile on the ads from the past half decade or so, and I find the picture to get - you guessed it - even more weird. Lincoln went from this weird value proposition luxury brand that had THE MOTHERDONKIN' TOWNCAR, to a brand that happened to offer some luxurious products. They've been no better than Buick, and yet, here they are trying to slap John Slattery (of Mad Men fame) and some retro-modern-future junk onto the brand. The Matthew Mcconaughey stuff was downright weird, trying to play them off as this post-modern luxury thing. Maybe? But when you go to the auto shows and stand in their stage, it does its best to look like a modern interpretation of a retro interpretation of the future. Think of the '60s World's Fair, crossed with Mad Men, and an Apple Store... You've got the idea. Sure, the Lincoln MKZ fits that. So does the MKC. But the MKS and MKT? Why even bother?
These days, the ideas of the executives and the marketing department seem to be coming together a bit more clearly with the new Continental. They want to be an American luxury brand. Nothing more, nothing less. What that means is largely up to what you think it should mean - and much of that seems to be high style, high comfort, high quality, and a not-very-high price. I get the feeling that Ford wants to make Lincoln not only a logical step up from the blue oval, but also a logical step up from Buick or Acura before you go onto an Audi or a Mercedes. And honestly, I don't think that that's a bad place to be.