Hair is what protects the largest organ--the skin--from potential damage from foreign objects and critters, which is why cavemen were extremely furry. If they weren't, they would have been scratched by vegetation and attacked by bugs even more. Lesson over.
True on the history lesson. However, we are no longer the neanderthals who required that much hair to protect our bodies from the natural world around us. Therefore, the vast majority of the hair on the human body has become largely unnecessary due to clothing, changes in society, etc....
Now, the the OP's original topic....
Just as being "plump" and having the most fair-skinned complexion was the height of beauty during the middle ages, being as hairless as possible has now become the height of beauty "standards". Largely for the same reason.
Being "plump" and of fair complexion in the Middle Ages were signs that one had the means to eat often and in great quantity. Being fair-skinned meant you were of sufficient means that you weren't out constantly toiling under the oppressive sun all day working. Likewise, hair removal can be a costly and time consuming process. It is something that must be maintained regularly for most people. Therefore, having the time, interest, and money to be able to upkeep one's appearance in as hairless a fashion as possible shows a certain implied higher level of "class" and "distinction" in today's society.