What exactly is critical listening? Who does it?

Individuals like me are perfect to answer this type of question because I'm an analytical listener by nature. Even when I listen for enjoyment, I still listen critically without even intending to. I'm listening deep into the music but I'm not trying to listen to every single note.

For instance, when listening to vocal, I listen deeply into the naturalness, the richness of the vocal. The slightest shift of pitch and tone and volume in each singing word. The transparency, the smoothness. The angelic voice. It's incredible. 

The term "critical listening" means different things to different people. For me it just means at that time, listening is the primary thing I am doing. I'm not talking on the phone, reading a book, watching the TV, doing chores, etc. Just listening. I don't have to be "critical" about what I'm hearing, nor do I have to hear every small detail. But I am intent on connecting with the music.

You know you're a critical listener when you have about twenty copies of the same album over different formats, re-masters etc.

Yes, listening to every little tiny difference in timbre, tone etc. brings me joy.