IMO it comes down to a bunch of different things. Power, value, running multiplats best out of all consoles (which is important to most gamers). Playstation is synonymous with gaming now and the brand carries a lot of weight globally, more in the home console market than the competition does. PS4 is less about gimmicks and more about having a great gaming platform. It also has plenty of multimedia features that suite that audience.
The console has a small form factor in relation to it's nearest competition, plus the controller is very comfortable and very fit for the purpose of the games being designed for it.
Sony's 1st party developers are well know for their quality and the brand is also known to put out great variety and quantity to boot. As much as people like to say otherwise Sony has announced a lot of exclusives for people to look forward to, the majority of those just haven't been from 1st party studios yet and Playstation doesn't have a history of losing exclusivity to other platforms.
There's no shortage of games either exclusive or multiplats.
Popularity also brings greater appeal, which in turn pushes sales even harder and all of these things combined are very much an unstoppable force for mass market appeal.
The missteps of Sony's competition also has an effect on the overall image of the system and brand as a whole.
TBH I think anything you can think about as a positive for Sony or negative for it's competition is why PS4 is as popular as it is.
