Emerson's essay "Self-Reliance" also emphasizes the Transcendental concept of the importance of the individual and each individual's intuition which is the "eye" that receives the "ray" of intuition. That Emerson stresses individualism is evidenced in the sentence that precedes,
Not for nothing one face, one character, one fact makes much impression on him, and another none.
In other words, each individual has his/her own intuitive experiences through he is "impressed" or not. But, in addition to this concept of the individual, Emerson expresses the idea of the Over-Soul of which all men are a part:
We but half express ourselves, and are ashamed of that divine idea which each of us represents.
Ralph Waldo Emerson's line, "The eye was placed where one ray should fall, that it might testify of that particular ray," reiterates what he has declared in his opening to "Self-Reliance." That is, to believe in yourself and your own thoughts, and to believe those thoughts are true for others, is of paramount importance. Indeed, Emerson's credo is "trust thyself." For him, and for another great Transcendentalist, Henry David Thoreau, the importance of independent thought and the openness to receive ideas intuitively are what make men individuals of worth.
In the part of the paragraph before the line you cite, Emerson is talking about how people need to be themselves. They have to realize that they are different from other people and that they should not try to be like other people. This is one of the Transcendentalists' biggest ideas -- that you need to be yourself and not try to be what others think you should be.
This ties into the eye and the ray. What this is saying is that each person has been made the way they are so that they can see their own truth. The eye is the whole self and the ray is the truth. So each person is put where they will receive the truth that is right for them.
I hope that makes sense to you...