There is a quality that some great musicians have; the ability to become engrossed in their performance, specifically when performing solo, with the effect that they become apart from the outside world. They enter their own space. I like to call it 'The Bubble'.
Think of a semi-transparent sphere, much like a force field in a sci-fi movie, enveloping a person. That's what the bubble would look like if you could see it.
When a musician is really in the zone they can enter the bubble and they become impervious to the outside world. The performance is here and now, but the current environment is unimportant. When you see Van Morrison onstage, a classic exponent of the bubble, you know that, for him, it doesn't matter if he's singing in his kitchen or in front of 10,000 people because, on a good night, he's in the bubble.
Some artists hardly ever, if at all, seem to use the bubble. Think of Mick Jagger, for instance. He's always performing out towards the audience. I can't imagine he is in the bubble very often.
An artist I have seen live recently who goes into the bubble is Lee Rogers. I'd imagine anything could be going on in the room and it wouldn't change his performance. Great stuff. Song + guitar + voice = the bubble.