Heart rates increase as the intensity of activity increases, as shown in the adjacent picture. This is because the working muscles demand more energy, so the heart beats increasingly faster in order to deliver the nutrients and O2 needed to meet these increased energy demands.
The normal resting heart rate range for an adult is between 60-100 bpm. However when a resting heart rate is greater than 100bpm it is called ‘tachycardia’ and when it’s below 60bpm it is called ‘bradycardia’.
These can both indicate possible heart conditions or complications and if you notice these in a personal training client of your's you should advise your client to have a medical check. The exception to this is that bradycardia may be present in extremely fit (international level multisport, triathlon, ironman etc) individuals and not something to be concerned about.