You didn't know about it? Well, you do seem more the manga type (as opposed to the anime type which is where DtB gets it's popularity from, lol)
Anyway, the basic plotline is this: At one point in time, "Gates" (walls, basically) surrounded Tokyo and part of South America (these Gates are known as Hell's and Heaven's Gate, respectively). The area within the gate is, essentially, a dome (though it looks like it is just the walls, while the sky still looks the same). However, it's a known fact that the night sky isn't the real night sky but a replacement. Each of the stars in the sky represents a Contractor. Contractors (whom are hidden from public knowledge in the first anime), are basically walking weapons. They express little to no emotion and are driven by logic (making them perfect for assassination or bodyguard type positions). All of these Contractors have a unique power and use of that power forces them to do an "Obeisance/Remuneration" (a compulsive act that they must accomplish; examples include smoking a cigarette, drinking a bottle of booze, blood letting, and breaking ones own fingers) afterwards. The plot focuses around Hei (and those around him, of course) who is a contractor that doesn't have an Obeisance and does allow emotions into his thought process (the reasons are explained in the first anime).
So yeah, people like it for it's interesting concept and because Hei is so good at beasting people.