In fact, I cannot understand folks that listen to music and work
I think you're confusing listening with having music on as background noise.
I have the same issue as the GP. The only music that I can use as "background noise" is classical. No lyrics, not even very interesting. I don't particularly like classical music, but it doesn't overtly bother me like jazz does.
If it's music I actually *like*, I'll get distracted from the task at hand and listen to it.
But, different strokes for different folks. I remember one time, my ex walked into the living room to ask me a question while I was sitting and reading a book. While talking, he picked up the TV remote, hit the Power button, surfed to a channel showing something vaguely interesting, put down the remote, concluded the exchange, and left the room. With the TV on. While I, on the other hand, don't turn on the TV unless I intend to watch it, because if it's on, I *will* pay attention to it.