As you know, of course there is no actual average person. Just a collection of central tendencies. But my experiences interacting with individuals for which I knew their exact formal normative standing for cognitive ability did show me that my preconceived notions of what a neurotypical learner of a certain age range should be able to do with regard to academics, general problem solving, oral language, etc. were not accurate. To my consternation, I realized that many of the people I had previously characterized as being not very bright were really quite typical. Perhaps partly because I didn't progress through the grades in a uniform manner, I hadn't formed a good idea of grade-appropriate skills, nor had I a sense of grades corresponding closely to age.
To your question, perhaps the simplest way of explaining average is to look at our grade expectations (which in North America are very much age-locked), and then consider that the average student puts effort into earning Bs and Cs, and requires explicit instruction and overlearning to become a fluent reader, and calculator of the four basic arithmetic operations, by the end of fourth grade.
There are non-academic qualities too, but they're harder to quantify.
