Well for one it improves blood circulation in the body. Once teh cold water hits your body then you begin breathing faster. For me however I have learned to take huge breaths which helps get even more bloodflow.

There's some studies that show that cold showers increase your white blood cell count. Which the more white cells you have the better for fighting illness.

Also it detoxifies you.

For example literally everyone in my family had gotten the flu when we got together around Christmas. I was the only one that did not get sick. My wife actually pointed out that it was because of the cold showers.