The sublunary sphere is a concept derived from Greek astronomy. It is the region of the cosmos from the Earth to the Moon, consisting of the four classical elements: earth, water, air, and fire. 
The sublunary sphere was the realm of changing nature. Beginning with the Moon, up to the limits of the universe, everything (to classical astronomy) was permanent, regular and unchanging – the region of aether where the planets and stars are located. Only in the sublunary sphere did the powers of physics hold sway.
Evolution of concept
Avicenna carried forward into the middle ages the Aristotelian idea of generation and corruption being limited to the sublunary sphere. Medieval scholastics like Thomas Aquinas - who charted the division between celestial and sublunary spheres in his work Summa Theologica - also drew on Cicero and Lucan for an awareness of the great frontier between Nature and Sky, sublunary and aetheric spheres. The result for medieval/Renaissance mentalities was a pervasive awareness of the existence, at the Moon, of what C.S. Lewis called 'this "great divide"...from aether to air, from 'heaven' to 'nature', from the realm of gods (or angels) to that of daemons, from the realm of necessity to that of contingence, from the incorruptible to the corruptible"
However, the theories of Copernicus began to challenge the sublunary/aether distinction. In their wake Tycho Brahe's observations of a new star (nova) and of comets in the supposedly unchanging heavens further undermined the Aristotelian view. Thomas Kuhn saw scientists' new ability to see change in the 'incorruptible' heavens as a classic example of the new possibilities opened up by a paradigm shift.
J. Barnes, Aristotle (1982)
M. A. Orr, Dante and the Medieval Astronomers (1956)
Thomas Kuhn, The Copernican Revolution (1957)
The Geocentric or Ptolemaic Notion of the Universe