The ergosphere, ironically, looks more like an ellipse from the side... In 3D, it looks more like a doughnut with no hole. In space this imaginary doughnut delimits a special region around rotating super-massive objects. The middle of this area is centered at the mass's center of gravity and is oriented in such a way that the axis of rotation of the object would emerge where the hole of the doughnut should be.
The ergosphere describes the space around the rotating object where the impressive gravitational pull of the massive object is potent enough to drag around space with its spinning (called frame-dragging). It is postulated that a person floating in this space without any initial kinematic energy relative to the surrounding space would be dragged around with said space—being anchored by position in it. Of course, relative to the ergosphere, he would be motionless; but relative to the space outside of the ergosphere, he could be moving faster than the speed of light (this greatly depends on the mass of the object an on its angular momentum).
This does seem to violate the rules of relativity
, but recall that relative to the space in which our poor observer helplessly floats, he would be motionless; it is the space in which he would be hanging that would be fleeing at super-relativistic speeds
—-relativity does not prohibit such an eventuality.
The Penrose Effect, like most ideas, of human provenance, proposes to abusively benefit energetically from this phenomenon; it's interesting though*. It is for this reason that this special region is named after the Greek word ergon, meaning, work: one could potentially extract work from the special properties discussed above.
*I am human after all...