The best explination: "Drifting is a combination of ballet and rice." (I use the word "rice" without reference to any ethnicity, only the "style" of car that it has been popularly referenced as).

Basically, it's car control. On a higher level, it's showing off. That's it. Just like a ballet, you're trying to take graceful lines making the car "dance" through corners. The "rice" aspect: you're just showing off (although all the "serious" drift cars are "riced out" as well). I guess the "dancing" part mostly applies, though.

So, my attraction to it??
1: it looks cool
2: it's a form of car control
3: it's something fun to do while not working on/ driving my SCCA racer (1:1).