The most common use for a heart rate monitor is to record intervals. Interval training means riding short efforts at high intensity, interspersed with rest intervals of easy pedalling. In time, this forces the body to adapt so that the intensity can be held for longer or can be increased.
Intervals can be ridden based on RPE (rate of perceived exertion), power (which measures the actual output of the body in watts) or heart rate (which measures the effect that the effort has on the body).
In an ideal world, power and heart rate are combined to show how much stress is required for the body to produce a given output - but the best power meters are expensive and heart rate monitors allow a rider to know that they're riding the efforts hard enough and the recoveries easy enough.
The intensity required during each interval will vary depending upon its length, but will usually be expressed in a 'zone' which is based on a calculation of the rider's max or threshold heart rate. So when training with a heart rate monitor, the rider just needs to know what BPM they need to hold for each interval to have the best chance at completing the training correctly.