August Pullman is an ordinary child at heart. He wants the same things that other kids want, such as friends and acceptance. On the inside, everything about August is ordinary. It is his exterior that is markedly different to that of his peers. When he says “the only reason I’m not ordinary is that no one else sees me that way,” he refers to the fact that people, especially those who have not gotten to know him, are unable to look past his disfigured appearance to realize that he is just like any other child.
There is an old saying that says that “beauty is in the eye of the beholder,” and what August is implying here is that normality is also in the eye of the beholder. The fact that he is unusual stems from people perceiving him to be unusual.
Prior to this quote, August provides background information, explaining that he feels ordinary and does ordinary things like riding his bike, playing ball, and eating ice cream. The only thing that makes his life abnormal is how other people react to him. It is due to these adverse reactions that August would take his one wish (if he had one) and wish for a normal face. He wants to be as ordinary on the outside as he is on the inside.
In a nutshell, what August means by this statement is that there is a huge divide between his normal heart and mind and his abnormal appearance. On the inside, he is just like any other child. On the outside, he is vastly different, and he wishes that this were not so.