What is the point of doing a cool-down anyway? You've put in those last few steps or repetitions, you're tired, you're hungry, and you have somewhere to be. So why bother with the final piece of the workout?
The scientific answer is simple. Any workout, is disturbing your homeostasis. The longer duration and more intense exercise creates a greater disturbance than shorter duration or less intense exercise. The role of the cool-down is to facilitate a smooth transition back to your normal state.
Prevents Blood Pooling
Exercise allows blood to be pumped freely throughout the peripheral parts of the body, and rhythmic movements in exercise (muscle pump) can actually help return that blood back to the heart. Abruptly stopping exercise without a cool-down period can allow blood to pool, which can lead to a light-headed feeling or even passing out. Cooling down does seem to help alleviate some nausea as well.
Keeps Blood Flowing
The active cool-down, doesn't just prevent pooling, but keeps blood flowing at a slower rate than intense exercise but a faster rate than at rest. This allows for more clearing of waste products, more shuttling of other by-products and transport of more oxygen and nutrients. This should all speed your recovery.
Intense exercise can wreak havoc on the alignment of muscles. This can take place on a larger scale when an entire muscle (or large numbers of fibers) is tight and pulling on joints and other muscles. That may cause pain and over time can cause serious posture and joint problems. This also leaves you more vulnerable to injury. On a small scale the fibrils (contractile components) of muscle fibers can be worked out of alignment, which impairs the function of the associated muscle fiber. Cooling down with light exercise and stretching can prevent these problems.
Can Improve Mobility and Flexibility
Muscles are much warmer following exercise, making it safer and easier to stretch them.
Hopping in the car and driving off in a hurry is a great way to feel light-headed and nauseated, before catching a huge cramp in your hamstring. All of this makes you a safe driver. This is what most of us do following a workout and it is far from optimal.
You've just run a hard workout on the track. Your next move would be a light jog of maybe 5 minutes if you're a beginner to 3 miles if you're fairly advanced. Don't run too fast or it is still part of the harder workout and not a cool-down. The pace should be determined by how you feel, but not any faster than a normal easy run. Follow the jog with a thorough static stretch.
You've just finished an intense weight training session. Your heart rate is up but not beating through your chest. Use your last few minutes in the gym to do some dynamic stretching and follow that up with a thorough static stretch, focusing on whatever body parts your workout used the most.