Well, I suppose that Dylan Thomas's poem affects each of us in different ways, i.e., we interpret it slightly differently, but to me it has always said to resist death, resist it with all your strength, don't give in to it, since life is so wonderful, so productive...and so unique: we only get one.
Thomas's father was a strong figure in his son's life, and this poem was written as his father lay dying, so the last verse lets loose all his anger over his father's seeming quiet acceptance of death. How many children have expressed anger at a parent's death? The parent seems to be deserting them, abandoning them-- or rather, fate seems to require this.
Thomas uses other images-- wise men want to continue influencing others, good men want to continue doing good deeds, grave men realize the joy they have not yet experienced-- and they all find the idea of death unfair. Of course, most people realize that death is just inevitable and that it is a 'good night' in some sense, but any thoughtful person would realize that our one experience here on earth is of much more personal value and would naturally fight to keep it.
I have provided links to the poem itself and to some more detailed analysis of it as a villanelle below.