Great question. What is interesting about this intensely memorable poem is that a typical elegy is a poem that mourns a death that has already occurred. Dylan Thomas creates something rather different with this poem, because it is an elegy spoken to a dying man, imploring him not to give in to death but to meet it head on in a spirit of defiance. Thus this poem is an excellent example of an elegy both in the sense of the word as the Greeks and Romans defined it, as a poem of meditation, and how the word is defined by today's audience, as a poem of mourning. The poem mourns the imminent death of the poet's father, but it also reflects on human mortality and the ways in which people face death. It speaks of such serious subjects as love of live and the battle against death.
Overall, however, one is struck by the lyrical solemnity of such lines as these:
Though wise men at their end know dark is right,
Because their words had forked no lightning they
Do not go gentle into that good night.
Good men, the last wave by, crying how bright
Their frail deeds might have danced in a green bay,
Rage, rage against the dying of the light.
It is such lines that combine the treatment of how we face death, mourning for a father, and the love of life, that make this poem truly great.