Also known outside the industry as a "disco ball," a sphere 3"-72" (20" is probably the most common size) in diameter covered with reflective tiles.
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When lit with a pinspot or other tight-beamed instrument, each tile reflects the source, creating "a thousand points of light" all over the room. Usually equipped with a mirror ball motor to rotate the ball, the reflections spin around the room.
Perhaps the most poetic description ever of a mirror ball ("Sometimes the lights were turned out except for a large glass sphere that hung from the ceiling. It would turn rather slowly about and filter the dusk with delicate rainbow colors.") courtesy of Tennessee Williams and Zachary Quinto: