Cooling Down

Cooling down after ballet class and before going home prevents injuries, while reducing the chance of next day soreness.
Going from one extreme to the next, such as sitting down immediately after a rigorous ballet class, can be dangerous.  A safe, gradual, decrease in the heart rate isn't allowed, and blood pools in the lower limbs.  The result is sore muscles, achy joints, and decreased stamina.  Obviously this interferes with your ability to dance your best.
An easy, short cool down should be relaxing.  Continue moving for at least five minutes, avoiding standing still or sitting down during this time frame after class.  Whatever you do, make sure the intensity is kept low.  You could walk around or repeat some moves done in class in a less strenuous way.  Once the heart rate has gone down you may sit to stretch, making an conscious effort to hit the muscles worked the hardest during class.  At this point be gentle and refrain from doing deep stretches, letting a minimum of one hour pass before indulging in those kind of stretches.
Warming up and cooling down play key roles in assisting the fight against injuries and staying in top shape.  Try to make both a part of your dance training.