Who does the poem "Do Not Go Gentle into That Good Night" address? What is the speaker saying?

The poem is addressed to the speaker's father.  In the last stanza, the speaker says, "And you, my father, there on the sad height, / Curse, bless, me now with your fierce tears, I pray" (lines 16-17).  The "you" in this line, then, is the narrator's father, a man who is, evidently, about to die; the narrator wants his father to fight against death and to remain alive as long as possible.

The "good night"...

The poem is addressed to the speaker's father.  In the last stanza, the speaker says, "And you, my father, there on the sad height, / Curse, bless, me now with your fierce tears, I pray" (lines 16-17).  The "you" in this line, then, is the narrator's father, a man who is, evidently, about to die; the narrator wants his father to fight against death and to remain alive as long as possible.

The "good night" in the poem is a symbol for death, and the speaker spends the majority of the poem detailing the ways and the reasons why all different kinds of men "Rage, rage against the dying of the light" (3).  Despite the fact that these men might understand death to be natural, in the end, none of them want or feel ready to go.  There is more they want to do, some past mistakes they want to rectify, etc., and so they "Do not go gentle into that good night" (1).  The speaker explains the way all these men refuse to go to death quietly in order to show his father that he should also resist death and fight to remain alive, that it is actually the natural and right thing to do.  In the final stanza, he implores his father to do this.