After any aerobic activity, the blood is pooled in the extremities, and the heartrate is elevated. The purpose of the cool-down is to bring the heartrate down to near-normal and to get the blood circulating freely back to the heart. Stopping abruptly could result in fainting or place undue stress on the heart. The cool-down should also include stretching to help relax the muscles which worked so hard during the activity. The cool-down stretches also increase flexibility, and might help to prevent DOMS (Delayed Onset Muscle Soreness) although this has not been proven.
This is part of the misc.fitness.aerobics Frequently Asked Questions page (FAQ).
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