The Euphrates River is the longest in western Asia and is commonly referred to as the "cradle of civilization." Hughes links himself to this history of a young world when there were few people populating the planet. There is a sense of innocence in the river in its early reference in this poem: providing water for bathing, which is itself symbolic of new beginnings and a return to innocence.
Hughes then moves to reference the Congo, the deepest river in Africa, winding through 11 countries. This river is symbolic of Hughes's deep connections to that continent; the connotations in this reference are also positive. The Congo provides a strategic place for the speaker to build his hut and soothes him to sleep at night.
The connotations shift in the third stanza to reference darker allusions. The Pyramid of Giza still exists as one of the Seven Wonders of the World, yet these pyramids which the speaker "raised" beside the Nile River were constructed with hard physical labor. There is a sense of pride in this line; the speaker's work produced something of greatness which stands as a testament of success thousands of years later.
And then the connotation grows darkest. The fourth river is the Mississippi, providing a path of transit for Lincoln's visit to examine the slaves' conditions. The undercurrent of slavery is in this river, and the "singing" is resonant of the songs of slaves on the Underground Railroad.
The rivers represent a progression of civilization in our world—the rise of civilization to a collapse of humanity. The speaker in this poem leads readers through a journey that begins in innocence and ends in tragedy—and he is connected to it all.