What is Air Rights?

Legal Definition
Air rights are the property interest in the "space" above the earth's surface. Generally speaking, owning, or renting, land or a building includes the right to use and develop the space above the land without interference by others.

This legal concept is encoded in the Latin phrase Cuius est solum, eius est usque ad caelum et ad inferos ("For whoever owns the soil, it is theirs up to Heaven and down to Hell."), which appears in medieval Roman law and is credited to 13th century glossator Accursius; it was notably popularized in common law in Commentaries on the Laws of England (1766) by William Blackstone; see origins of phrase for details.
-- Wikipedia
Legal Definition
The right to control the air space on your property. Reasonable use by neighbors or an aircraft is allowed. It can be bought, leased, sold, and transferred like with any rights.