Density altitude is pressure altitude corrected for non-standard temperature. Stated in a more pertinent way, density altitude is the theoretical altitude within a standard atmosphere where the air density is equivalent to the measured air density.
Practically speaking, density altitude is most useful for comparing aircraft performance throughout a range of atmospheric conditions. When an aircraft flies in a given air density (as determined by atmospheric pressure and ambient temperature), the density altitude is the true altitude within a standard atmosphere in which the aircraft will have the same performance characteristics of its current true altitude. For example, if that aircraft was at a density altitude of 2,000 ft., it will perform as if it was in a standard atmosphere at 2,000 ft. even though its true altitude may be significantly higher or lower than 2,000 ft.
Because dense air is advantageous for improved aircraft performance, low density altitudes always coincide with high air density. High density altitudes are caused by low air density and always result in decreased aircraft performance.