The "Stranger" and the "Young Girl," the two masked figures in the play, are eventually revealed to be the ghosts of Diarmuid MacMurrough and his wife Dervorgilla, who were historical, though almost, legendary, figures in Irish history. In the 12th century, Diarmuid, one of a host of local chieftains of one of the Irish tribes, stole another prince's wife. When the offended husband threatened to retaliate with force against Diarmuid, he called in a Norman adventurer named Strongbow, and that in turn led to the arrival of other Normans. This turn of events worried the English. Henry II then became the first English king to sent in colonizing forces--the beginning of 800 years of oppression.
Significantly, Yeats sets the play in 1916, just after the Easter Rising at the General Post Office in Dublin (discussed in your "Wee Bit o' Irish History"). The "Young Man" is a patriot who participated in that event. When asked to forgive Diarmuid and Dervorgilla for what they did, he almost does so but finally refuses. According to some critics, Yeats associated this kind of brittle, unyielding stance with his beloved Maud Gonne, while he tended to think that such national self-hatred was part of Ireland's problem.
Note the year the play was written: 1919, three years after the Rising, yet still a couple of years (but who could then say how many?) from seeing its reward.
When you read the play, consider the significance of the masks. Consider also the circular patterns--the endless repetition the lovers are in, the recurring image of the music, "Red cocks, and crow!" With this example of Yeats' work we'll get an introduction into his complex system(s) of religion, mythology, and prophecy, all of which are embedded within a very formalist aesthetic.
Specifically about the way the trope of "dreaming" works in the play, Yeats had a definite idea in mind. He wrote in the introduction to his Four Plays for Dancers,
"The conception of the play is derived from the world-wide belief that the dead dream back, for a certain time, through the more personal thoughts and deeds of life. The wicked, according to Cornelius Agrippa, dream themselves to be consumed by flames and persecuted by demons; and there is precisely the same thought in a Japanese `Noh' play, where a spirit, advised by a Buddhist priest she has met upon the road, seeks to escape from the flames by ceasing to believe in the dream. The lovers in my play have lost themselves in a different but still self-created winding of the labyrinth of conscience. The Judwalis [a fictitious Arab tribe? probably invented by Yeats or some of the mystics that he associated with] distinguish between the Shade which dreams back through events in the order of their intensity, becoming happier as the more painful and, therefore, more intense wear themselves away, and the Spiritual Being, which lives back through events in the order of their occurrence, this living back being an explaration of their moral and intellectual origin.
"All solar natures, to use the Arabian terms, during life move towards a mroe objective form of experience, the lunar towards a more subjective. After death a lunar man, reversing the intellectual order, grows always closer to objective experience, which in the spiritual world is wisdom, while a solar man mounts gradually towards the most extreme subjective experience possible to him. In the spiritual world subjectivity is innocence, and innocence, in life an accident of nature, is now the highest achievement of the intellect . . . .
"The Shade is said to face out at last, but the Spiritual Being does not fade, passing on to other states of existence after ithas attained a spiritual state, of which the surroundings and aptitudes of early life are a correspondence. When, as in my poem, I speak of events while describing the ascent of the Spiritual Being, I but use them as correspondence or symbol. . . .
"[I]n making the penance of Dermot and Dervorgilla last so many centuries, I have done something for which I had no [explicit] warrant . . . , but warrant there certainly is in the flok-lore of all countries. At certain moments the Spiritual Being is said to enter the Shade, and during those moments it can converse with living men, though but within the narrow limits of its dream."