Plain English Meaning
Air that is packed tightly with molecules. The colder the air and the closer to sea level, the more molecules are crammed into each cubic foot, and that thicker air helps the wings, propeller, and engine all work better.
Full Definition
A condition in which a given volume of air contains a relatively large number of air molecules, typically associated with cold temperatures, low altitudes, low humidity, and high atmospheric pressure. High-density air provides more lift for a given airspeed, more thrust from the propeller, and more power output from a normally aspirated engine.