It is often helpful to look at such isolated quotes in the context in which they are presented. Doing this often yields clues that helps us to understand their meaning. Let us do this by considering the first stanza:
Do not go gentle into that good night,
Old age should burn and rave at close of day;
Rage, rage against the dying of the light.
Note the way that this opening stanza of this powerful elegy contains two metaphors that are used to compare life and death, as death is compared to night and life to light. Thus the meaning of the centre line becomes clear. As we approach our death, Dylan believes that all people should find a way to fight against death, to metaphorically "burn and rave" against it. This, according to Dylan, is what unites all mankind as death approaches and we all struggle with all our might against the encroaching power of death. The use of diction is particularly important, as the words "burn and rave" express the grim battle that so many face against death and capture the anger and passion that is necessary to be successful in that fight.