What three specific ideas does Du Bois present in The Souls of Black Folk?

The three most unique and perpetually relevant concepts to come out of W.E.B. Du Bois's The Souls of Black Folk are the following: double-consciousness, the veil, and the color line.
The concept of "double-consciousness" is described in the first chapter, "Of Our Spiritual Strivings":

After the Egyptian and Indian, the Greek and Roman, the Teuton and Mongolian, the Negro is a sort of seventh son, born with a veil, and gifted with second-sight in this American world,--a world which yields him no true self-consciousness... It is a peculiar sensation, this double-consciousness, this sense of always looking at one's self through the eyes of others, of measuring one's soul by the tape of a world that looks on in amused contempt and pity (Du Bois 5).

Notice how he mentions all of the "races" and cultures known to have produced great civilizations. The Negro "is a sort of seventh son," a forgotten child whose own accomplishments go ignored. He uses, too, the modern term "Negro," when "colored" was the de facto designation for black people during the time in which he writes this. He introduces the concept of the veil here as well, which I will later explain.
"Double-consciousness" is uniquely both a "second-sight," but also a state of mind which provides "no true self-consciousness." This is to say that black people have difficulty forming a self-image without being beholden by the white gaze. Black people are hyper-conscious of what white people think, worried that the bad behavior of a single individual will spoil the perception of the entire race due to the white supremacist's tendency to view all blacks with "amused contempt and pity."
Thus, one is conscious of oneself as others (i.e., whites) see him or her and, unfortunately, "measures" oneself by that conception. This consciousness places black people outside of the American mainstream, though the black American is thoroughly a product of America. The goal is to "merge" these identities, never to abandon one for the other:

He would not Africanize America, for America has too much to teach the world and Africa. He would not bleach his Negro soul in a flood of white Americanism, for he knows hat Negro blood has a message for the world. He simply wishes to be both a Negro and an American... (Du Bois 5).

The "veil," in a metaphorical sense, is a manifestation of how black people learn to see themselves as both black and American. The veil signals separation. According to Du Bois, "the veil" is what makes one "different from the others...shut out from their world..." (Du Bois 4). He had no "desire to tear down that veil," but "to creep through" (4). This means that he does not want to dismantle what makes him different -- he embraces that. However, he does not want his difference to preclude him from inclusion into all of the rights and opportunities afforded by those who are not viewed as "different."
The veil also signals that one is somehow obscured, or not clearly seen by others. This inability to be seen by others, as fully human and individual, is what results in the color line. The color line is the social result of whites viewing black people as thoroughly different -- with goals and values that are somehow separate from their own -- and as less worthy of equal recognition.
 
Source: Du Bois, W.E.B. The Souls of Black Folk. New York: Penguin Books,   1996. Print.