This passage from "Self-Reliance: by Ralph Waldo Emerson concerns a man's integrity and wholeness of experience. He writes,

Not for nothing one face, one character, one fact makes much impression on him, and another none.  This sculpture in the memory is not without preestablished harmony.  

 Emerson begins his essay by defining genius: 

To believe your own thought, to believe what is true for you in your private heart is true for all men--that is genius.

The meaning of the passage that is recorded in the question comes from an examination of this definition of genius along with the preceding lines about the harmony of memory cited above.  "Self-reliance" involves the "proportionate," that which is balanced between one person's thoughts and the harmony of these thoughts with those of others while one also "accepts the place the divine Providence has found" for him/her.  As a part of the Over-Soul which Emerson, like other Transcendentalists, believed in, man arrives at truth that is "faithfully imparted" and "proportionate" with others and with God.  This is, indeed, truth; it is not what is "made manifest by cowards," for they would alter the truth out of fear. 

In this paragraph, Emerson is talking about how people should be true to who they are.  They should realize that they are unique and should be brave enough to stand up and testify about their own particular vision of the truth.  Just before the lines you cite, Emerson says

The eye was placed where one ray should fall, that it might testify of that particular ray. Bravely let him speak the utmost syllable of his confession.

However, Emerson says, most people are afraid to do this because they are not good enough people.  They should trust that their part of the "divine idea" is good and right for them (the first part of your quote).  However, they do not because they are cowards -- they are not truly "men."

So your quote means that people should stand up and give their own version of the truth, but they do not because they are cowards.