Normal is statistical. You score something on a particular measurement range, and the stuff that is in the middle of the scores, and occurs most often is considered normal.
With humans, it’s tricky, because you can’t really determine what normal is until you measure something. There are so many aspects to humans, and most of them are not yet measurable.
So people choose something like a standardized test or an IQ test, and let that stand as their measurement of normality. They do it because it’s all they can do, and something is better than nothing (usually they have to deliver services). But as Seeker pointed out, a person can be considered retarded on one measurement scale, yet perform better than average on another. But, we still call them retarded. How much sense does that make?
Personally, I hate the idea of normality, because I am off the scales by some measurements that I think, arguably, don’t require treatment. Basically, I’m bonkers, and I have the certificate to prove it. I’d prefer not to think of myself that way (now seeker is going to beat me up for even using that description about myself), but the diagnosis is on the charts, and will be forever on, now.
The problem with having ideas of normality, is that we become less tolerant of deviance. (Deviance is another statistical term, and it measure how different a measurement is from the average). Usually people consider their own kind to be normal, which makes others who look, act, or think different to be the deviant ones. Then they kill the deviant ones (or, at least, that has been the historical pattern).
I’m a deviant, so some lynch mob could find out, and decide I’m too dangerous to live, and come and kill me unless I do it first. My family will not appreciate that. Neither will my employer. There might even be a friend or two who shares their dismay, but I wouldn’t count on that.