The idea of the cool-down seems to have originated with a popular theory — now known to be wrong — that muscles become sore after exercise because they accumulate lactic acid. In fact, lactic acid is a fuel. It’s good to generate lactic acid, it’s a normal part of exercise, and it has nothing to do with muscle soreness. But the lactic acid theory led to the notion that by slowly reducing the intensity of your workout you can give lactic acid a chance to dissipate.
The article goes on to say that it does nothing to relieve muscle soreness or tightness either.