This quote appears in the second paragraph of Emerson's famous essay. He begins the paragraph by discussing the fact that each man comes to a point in his life when he realizes that the power to know and to do lies only within him. Emerson states that "imitation is suicide," and in doing so, he establishes his thesis to be supported by the quote from your question.
The quote specifically refers to the idea that an individual's perception is solely his own. There is no standard or reason for why some things, people, or ideas leave an impression and why others do not--it is simply up to the individual to interpret what he sees with his "eye." Emerson believes that not only must a person be reliant upon self in providing basic necessities, but he must also be self-reliant in his thinking, beliefs, and perceptions.
The correct quote is
Not for nothing one face, one character, one fact, makes much impression on him, and another none.
The meaning of this quote is very much in line with the point of the whole essay. In this essay, Emerson is saying that people should do what their own conscience tells them, not what society says to do. Just before the quote you mention, Emerson says that people need to understand that "imitation is suicide." This means that people must do their "own thing" if they really want to be people.
Your quote means the same thing. It says that there is a reason that some things (some faces, characters or facts) make an impression on us and other things don't. The reason is that we are all different. Because we are all different, we must do what our own minds tell us.