I think what they mean in societal terms is just what is "socially acceptable". Whatever falls into the realm of things people are used to.
In scientific terms it is what falls in the category of the most statistically commonly found. So if some scientist were studying butterflies of a particular species and found there were way more red ones than blue ones, they'd come to the conclusion red was "normal" and blue was an anomaly or a rare variant. Or if they studied the behavior of the butterflies and 99% of them liked to sit in the sun in the morning 99% of the time, they'd conclude this was "normal" butterfly behavior.
In short, "normal" is just a word, not a truth. When it comes to mental "disorders", many disorders seem to be so common among people, I believe they've been labelled disorders only because 1) the science of psychology is still very new and has much to learn and 2) the idea of a 'normal person' is a fiction we're all led to believe exists.