Keurig is really convenient and cheap.
A Keurig machine, regardless of model, doesn't take much space. You can almost certainly put it somewhere in the kitchen or an office and just leave it there. By contrast, a machine that can grind beans is much larger, and you need to carefully plan for its presence.
The machine is obviously cheap -- most models are under $100, and only "high end" models with questionable features but not necessarily better taste are over that number. The pods are cheap -- you can easily get them for less than $0.5/pod, sometimes $0.4/pod. By comparison, Nespresso capsules are generally around $0.8-1/capsule. Note that I didn't say it's cheap per "unit coffee" -- there is usually less than 10g coffee in each pod (and that varies) and can be really weak for the amount of water used. This is why people suggest that if you have to use Keurig, use the least amount of water allowed.
Of course Keurig coffee doesn't taste the best. But most people aren't aware (even though they are likely able to tell the difference), and at the end of the day, the machine gets the job done. What makes them popular is cost and convenience. Like so many other products on the market.