The phrase’s meaning is simple: one should look at the evidence and believe what they see with their eyes. It also refers to skeptics, who are always searching for proof.
Hamlet once said to Horatio, “There are more things on heaven and earth, Horatio, than are dreamt of in your philosophy.” By writing this, Shakespeare meant that one must believe what he or she sees. Even if they previously did not think so, the real evidence should change their mind. In the beginning, Horatio denied the existence of the Ghost, but later, he saw it with his eyes. His attitude changed, and he said that he would not believe it if he did not see it by himself. The appearance of the Ghost terrified him and brought a sense of unease in his heart.
The phrase can also be referred to as skepticism. Being a skeptic does not mean to disbelieve everything if there is no proof. Such quality should force a person to seek new experiences, learn new things, and challenge beliefs. Horatio was an educated person with his philosophy. He was a skeptic who denied the claim because he did not have evidence. He did not believe people because their words were unreliable. In general, the new things may be scary, like the Ghost appearance terrified Horatio, but there is no need to refuse them.