Why take a cooling down period?
Cooling down helps your body relax. You gradually lower your heart rate and bring your blood pressure back to normal. In addition, the waste products produced through exercising are removed. This reduces muscle soreness and stiffness after exercising and lowers your risk of injury.
How do you cool down properly?
Cooling down after cardio training could involve a few minutes of leisurely walking, cycling, rowing, etc. followed by a muscle massage. It doesn't have to be a massage by a professional! You can do a good job of massaging the muscle groups in your arms, shoulders and legs yourself using a foam roller or massage stick. Also, don't forget to do some stretching exercises.
Even after strength training, you can close out your session by cooling down with a few minutes on a cardio machine that works the same muscle group that you just trained. Or you can gently perform the exercises you just completed with a lighter weight for a few minutes, paying close attention to your inhale and exhale. This helps to lower your heart rate and blood pressure. Then do several stretches to help your muscles relax and, finally, drink plenty of water. Make sure you restore your body's protein and carbohydrate levels, e.g. by eating a protein and carbohydrate-rich meal or snack.
If you worked out so hard that you're completely wrecked, first sit down and drink some water before you start to cool down.