The dominant theme of Thomas's poem concerns the love of life and, specifically, the struggle against death. The phrase "Old age should burn and rave at close of day" appears in the second line of the poem. Here, "old age" is what should be burning and raving.
"Old age," or the slipping away of life, is the principle antagonist of the poem. It refers to being old in age as well as being tired. We find in the final stanza that the poem is addressed to the poet's father, who is "on the sad height" of his spent life. The burning and raving mentioned in the second line should also apply to him. These words are suggestive of madness but also conflict. That is, there is a maddening sense, at the end of one's life, that all the struggle and achievement of life has been for naught. At the same time, there is a sense that we should reject that conclusion, insist that life has meaning, and fight to continue to be alive, even though our life is being consumed or burned up by the passage of time.
In this sense, the "old age" that is being referred to here is not simply his father's but the old age of all people, and the poet's assertion that we should fight against "the dying of the light" is a statement about the human condition itself.