Why does the heart beat speed up after exercise?

When presented with a training stimulus (or even the thought of a training stimulus), your heart rate will naturally begin to increase. This is the body's way of preparing for a stressful situation where its survival might be called into question. Understand that your body cannot differentiate between running around a track and running from a hungry lion--both are situations equally deserving of a rapid increase in heart rate to prepare it to "survive" the encounter.

The reason why your heart needs to beat faster as the physical demands on the body increase has to do with the concept of sufficiency. Generally speaking, your body only wants to perform the minimum amount of work to complete a task. When sitting around watching television, your organs and tissues do not require that much oxygen to continue functioning. Thus, your heart will beat slowly, conserving its strength. To the contrary, when exercising, your body requires much more oxygen to keep your body moving at rapid rate--causing your heart to speed up to meet the demands.