That they shouldn't have any exceptional abilities. There are good arguments for each side. This is great. This can be an entertaining game to play. Some people give their characters very high ability levels without providing any good reason as to why such a highly skilled person would be wandering around the world getting involved in all sorts of odd plots instead of practicing his or her profession.
Some people confuse the two arguments.
I believe that these are two entirely different statements. These are two different concepts which often get confused. The mythical average guy off of the street would not have exactly average ability in all of his skills - in fact, a person who isn't poor or good at anything would be fairly unusual. A large number of people in the world are above average. Having a PC be above average is nothing unusual.