Do not go gentle into that good night,
Here Thomas begins a straightforward command. Notice that the syntax of the sentence (a command!) mirrors the meaning--Don't go gently into "that good night." You probably know that night and death are very much alike, the darkness of closing one's eyes, the fact that the sleeper is in a prone position, the inability to know what is there in sleep or in death. The speaker in the poem is giving a message which is not a peaceful one about death: don't accept it, don't glide into it without a fight at the very least!
Old age should burn and rave at close of day;
Many people describe old age as the "golden years" when people slow down and take it easy. Again, Thomas want to subvert that common image of old people, and of the acceptance of death, by playing with the image of burning and raving. These are not glowing embers of a dying old fire; people should not just accept the going out of the fire, but kick it up a notch: burn. The verbs are especially important here: full of action, yes, but also senses. Burning is heat, light, smell, sound. Raving is action and sound.
Rage, rage against the dying of the light.
Here Thomas is beginning the repetition he'll continue throughout the poem: a command to defy death, "the night" from line one, the "dying of the light" here. You'll see that the rest of the poem goes on to describe the different kinds of people and how/why they should rage against the dying of the light. Notice again the command form in syntax, and choice of verb: "rage." Do not accept death.
The first three lines provide the basis of the thematic exploration of aging, death, and resistance which are reiterated throughout the poem. The title and first line of the poem help to bring this out. It seems to be a call or demand from one person to another to resist or fight the acquiescence to another force. In this setting, a loved one is speaking to another one to resist the force of death which is defined as a "good night." Fearing that the succumbing to death will render one as passive and devoid of the uniquely human qualities of resistance and intensity, the second line finds the speaker suggesting that there should be a certain type of "rave" and continual stoking of the life force (seen as fire in the term "burns") when confronted with the inevitable force of death. The third line of the stanza is repeated throughout the poem in its demand of resistance against the forces of silence and death. The first stanza sets up Thomas's assertion that fighting and intensity are youthful qualities that should never be lost nor silenced no matter the adversary.