Warm ups increase the blood flow, increases the amount of oxygen in the blood, stretches muscles and tendons, gets the body ready for exercise more gradually rather than a sudden shock, and more.
At least that is what I have read. My own experiences mirror these texts.

As for cool downs, I do this more for the fact that I tend to overheat when I stop riding no matter the season. Plus, for commuting it helps to keep you from sweating buckets when you show up at work. In winter I tend to use a mixed mode commute with a bus or light rail taking half the distance. If I do not cool down and immediately jump on the train or bus I will overheat in no time flat. Then my stomach looses it.