What is the relationship between heart rate and fitness level?

The relationship between heart rate and fitness level is variable for individuals. The ability to push more power at a lower heart rate indicates that you are more fit. Your heart is a muscle and when it grows stronger through endurance training, it is able to pump more forcefully, pushing more volume of blood through the muscle per beat. This is a positive training effect, as the body improves efficiency, by being able to deliver the same amount of oxygen, transported by red blood cells, to working muscles with fewer heart beats. Another positive indicator of fitness is being able to work aerobically for longer periods of time at higher intensities. This is referred to as increasing lactate threshold. Keep in mind that hydration, nutrition and rest play a major role in rate of perceived exertion and heart rate. So you will not necessarily see lower heart rates on subsequent field tests, in fact you might see higher heart rates as reflective of your increased lactate threshold.