ACE defines cardiorespiratory fitness (which I think is a more precise term, and underlines the inherent interplay of the heart and lungs) as “…how well the body can perform dynamic activity using large muscle groups at a moderate to high intensity for extended periods of time.” from the ACE Personal Trainer Manual.
If you want a less precise definition you might say aerobic fitness refers to the ability to sustain work over time that requires increases in oxygen consumption.
Think of the VO2 equation, delivery times extraction…..VO2=delivery x extraction. The most significant adaptations that occur with “aerobic” training are at the extraction variable. Adaptations that occur in the mitochondrial enzyme complex that enable one to more efficiently and with a greater volume utilize oxygen. Working hard, working long, working often with rhythmic, large muscle movements is the most effective way to facilitate these adaptations.