It is typically difficult to know what prompts a writer to address a particular topic. Often, they might comment on some aspect of the society in which they live, or, alternatively, they might comment on some element of their own personal life that strikes the writer as particularly interesting, difficult, or complex. "Do Not Go Gentle into That Good Night" was published in 1951, and the poet's own father died in 1952. Therefore, it seems incredibly plausible that Thomas was writing out of a sense of personal pain and struggle. If he was watching his own father approach the end of his life, we can certainly understand his use of apostrophe in the poem which, we learn in the final stanza, is addressed directly to the speaker's father, who is near death.
In the poem itself, the speaker describes the behavior and feelings of all different sorts of people as they near death: the wise, the good, the wild, and the grave (or serious). Each of them feels that they did not do enough; they did not have enough of an impact; they did not live fully enough; they did not take advantage of all of life's opportunities; and so each must "rage[s] against the dying of the light," a metaphor for death. In the final stanza, the speaker directly addresses his father, suggesting that he, too, should fight death, that his "blind eyes" could still "blaze like meteors and be gay." One must continue the fight to live.