Plain English Meaning
How thin or thick the air actually feels to the airplane right now, expressed as an altitude. On a hot day at a low airport, the air can feel as thin as the air thousands of feet higher up, and the airplane performs as if it were up there.
Full Definition
Pressure altitude corrected for non-standard temperature. It is the altitude at which the standard atmosphere would have the same air density as the air the aircraft is currently flying through. As temperature rises, humidity rises, or pressure falls, density altitude increases and the air becomes thinner.