Focus is extraordinarily important to a musician. To be in the "now" every moment. It's when we lose concentration that we make mistakes, have memory lapses, etc.
I also don't think it is a completely natural ability for most people. I believe it requires practice just like technique. Playing very, very slowly, listening to each note is one way to practice. As soon as your mind drifts off, stop, try to identify what happened and when. Did your fingers just take over? Where you listening to what you were playing?
I find, practicing with my eyes closed helps me to focus on the music. I'm sure others might have some other suggestions. For me, "really listening" ti the music helps me maintain focus.