Daniel Dennett came up with this expression in his philosophical exploration of human identity: Consciousness Explained. He used it to describe the concept of Cartesian dualism.
In his famous paradigm: 'Cogito ergo sum'(often translated as 'I think, therefore I exist'), Rene Descartes concluded that there is a sentient part of ourselves outside the material world, that is able to observe that same material world, including the material, physical part of ourselves.
Daniel Dennett describes this concept with the image of a theater (of the 'outside' world), where some part of us, the sentient part, sits as an audience and watches the show.
In a sense,Descartes disconnects the 'I' in 'I think..' from the thought process itself. As if there is an ultimate identity that is not part of our stream of consciousness. One could argue with that by stating that if there was no I there would be no thought at all.
Dennett continues from there on to the conclusion that Descartes' 'I' is a mere side-effect from our thoughtprocess. The image of a theater somewhat ridicules Descartes' theory but it is only used to reveal the weak spot in it's foundation.