Both doctors and coaches use average heart rate to provide information about a person. For a doctor, it can tell much about someone's overall heath, in particular the health of their cardiovascular system, while for coaches, it is a simple indicator of fitness.
Average heart rate can be taken at different times, depending on the information you want to get from it. Resting pulse, taken when you are sitting or lying down, calm and relaxed, is a simple indicator of how fit you are, and also whether you are either unwell or overtraining.
The best way to get information on average heart rate is from a monitor. As long as there is a good connection between the chest strap and your chest, these are very accurate - much more accurate than taking your pulse at your wrist or throat.
The best time to take your resting pulse is first thing in the morning, when you wake up. Simply getting up and walking around your bedroom will cause your heart rate to rise, and other factors, such as the caffeine in a cup of tea or coffee can also cause an increase.
Taking your pulse regularly allows you to get a true picture - by comparing it over days and weeks you will be able to see if you are getting fitter, as measured by a slower pulse. Alternatively, if your pulse is 10% or more higher than normal, it indicates either that you are unwell, or that you are overtraining - time for a day off!