"You see but you do not observe." Sir Arthur Conan Doyle.
The significance of the quote is that it says people often look around and see things but not pay attention to this detail. For Christopher, he can see things no one else can physically but he cannot fill in the blanks. For other characters in the book, they cannot see what Christopher see's, they only glance. These are some examples of the quote from the book.
Christopher had to be told specifically what happened to his mother. When Christopher runs into Ms.Shears, she eventually tells him that his mother had an affair with Mr.Shears. She tried being discrete about it saying that they "saw each other" or "liked each other" but Christopher did not understand. Eventually she said that they had an affair. In a way Christopher saw what she was saying but did not observe it.
Later on Christopher discovered some letters addressed to him from his mother that were recent. The letters said that she was with Mr.Shears and they lived in London. When Christopher read this he thought this was a mistake. He thought that she was another Christopher's mother and not his. Then when he read on he discovered that it was his own mother. He saw the letters but did not make the connection between them.
Christopher can often see what no one else does. Because of his Aspergers he likes to study his surroundings. He can tell if a telephone pole has new scratches on it immediately as soon as he sees it. The other characters do not see this they just see a telephone pole. They do not take in their surroundings all they do is look at them. The people see but do not observe.
All of this is true in real life too, this is not just fiction it is truth. In an average day most people just glance at life and don't take the time to really observe and study their life. We have become so absorbed in technology, social media, and work. There is little time cut out in our day to just stop and take in the world around us. If we did we could be more aware of economic, geographic, and national issues. We could actually make a significant difference in the world instead of being a sheep in the herd. It is true that we see but do not observe.