Controversial statement ahead: Beats deserve every bit of success they've achieved up to this point.
They identified a demand for higher quality headphones that was not being properly met at the time by existing high-end headphone manufacturers. Before Beats came around, the only places where you could actually demo quality headphones were at brand-specific speciality retail stores in larger malls like Bose, Sharper Image, or Bang & Olufsen. In larger chain stores where the vast majority of people shopped for electronics (Best Buy, WalMart, Sears, fye, even Apple stores), they rarely stocked those high-end headphones and whatever was for sale or being demoed was mediocre at best.
The effect is that most people, even those who would be interested in paying for much better headphones than they currently owned, likely never knew what they were missing. And the only way one could come across high-end headphones were if they actively seeked them out, because the market at large thought that only a small niche were interested in paying several hundreds of dollars for high-end headphones. Those manufacturers were happy not marketing and waiting for people to come to them rather than trying to appeal to a larger audience.
So Beats makes a huge investment into a distinctive design and marketing to make the product seem fashionable to a broader audience, but more importantly, getting demo stations into as many stores as possible. To many people, trying on a pair of Beats at a demo station in Best Buy or wherever was the first experience they had with anything approaching a quality pair of headphones, and to those people, Beats were revolutionary. While the marketing, celebrity endorsements, and the fashion statement elements of Beats certainly helped, it only helped because the core product was solid and to many people, was worth the money. All the advertising and celebrity endorsements in the world wouldn't do much if Beats didn't sound much better than whatever you got for free with your phone or MP3 player.
Sure, there always were (and still are) several headphone manufacturers that routinely make headphones with vastly better build quality and demonstrably more accurate sound reproduction with a smaller price tag than Beats can. For people who are willing to go out of their way to do some research and don't derive any value from the fashion statement aspect that Beats have, there are plenty of better products on the market. But if those manufacturers are unwilling to put their products in front of people in the way Beats does, then to most people (people who want to try before they buy or haven't been convinced of any reason to spend three figures on headphones), those other manufacturers might as well not exist. The fact that Beats has carved out roughly 70% of the high-end headphone market and grew that market significantly pretty much by itself in the past five years proves that.
At a time when the conventional wisdom across the entire electronics industry was that only a tiny niche of customers actually cared about sound quality, the people behind Beats believed differently and put a lot of money on the line to properly prove it. Hell, even Apple bet against it. They easily could've been selling $500 headphones for years had they put the work in, but they never did.
I never used Beats headphones but Beats Music is great, IMO the best music streaming service right now.
Yet another reason for Apple to buy Beats. Apple has a long history of buying up smaller upstart music services (I miss you LaLa) just to get rid of future competition, and Beats Music is a strong service that could have been serious competition to iTunes. It seems that Beats Music will still go on, but at least Apple won't be suffering for it.