As runners and cyclist we get exposed to multiple weather conditions. Our ears are very sensitive to infection and covering them during our outdoor activities keep us safe from infections
More over, head band also called as bandana helps in keeping your head cool during long run as it absorbs sweat and then no need to pour water over head to cool down.
When one starts wearing it may be uncomfortable but as you wear it more you will start liking it.
You can use warm cap to keep your head warm during cold seasons and it works dual purpose to cool down as your temp increases.
You can also initially use it as neck warmer and then use it over head during running.