Both a warm-up and cool-down period are essential parts of any exercise session. Warming up brings about important physiological changes that reduce the risk of injury, while also preparing the body for higher levels of effort and energy utilization. 
• Leads to efficient calorie burning by increasing your core body temperature 
• Produces faster, more forceful muscle contractions 
• Increases your metabolic rate so oxygen is delivered to the working muscles more quickly 
• Prevents injuries by improving the elasticity of your muscles 
• Gives you better muscle control by speeding up your neural message pathways to the muscles 
• Allows you to work out comfortably longer because all your energy systems are able to adjust to exercise, preventing the buildup of lactic acid in the blood 
• Improves joint range of motion 
• Psychologically prepares you for higher intensities by increasing your arousal and focus on exercise 

Blood tends to accumulate in the lower body when a vigorous exercise session is stopped abruptly. With reduced blood return, cardiac output decreases and lightheadedness may occur. Because muscle movement helps squeeze blood back to the heart, it is important to continue lower level physical activity after the exercise session is completed (i.e. the cool-down period). 

The best activities for both are simply to work at a much lower pace in an aerobic/cardiovascular activity that you are using for training. Examples include slow cycling on a bike or walking on a treadmill. As a general guideline, a 5 – 10 minute session should be dedicated for both warming-up and cooling-down.