William Wordsworth was a Nature poet who worshipped Nature as his God. For Wordsworth, Nature was his main source of spirtual comfort and escape from all the cares of this world. His association with life giving and life sustaining Nature began even when he was only a child and remained with him till his death.
In this short lyric, the 'rainbow' symbolizes the life sustaining and life nourishing goodness of Nature. The sight of the beautiful rainbow which he saw when he was only a child is deeply etched in his memory and the same joy that he experienced when he saw it as a child contiunes to remain with him through his adulthood. He desires that this same childhoood joy should continue to sustain him even in his old age. Wordsworth says that he would rather die than not being able to experience the same joy that he experienced when he saw the rainbow when he was a small boy after he becomes an old man.
The memory of the beautiful rainbow and its pleasant associations form the link between his childhood, adulthood and his old age:past, present and future. Wordsworth concludes the poem by expressing the desire that each day of his existence be linked with the next by beautiful and simple natural sights like the rainbow.
The rainbow which he saw when he was a child becomes the 'objective correlative' in the literary text which recalls to his mind the pleasant memories associated with the beautiful rainbow.
In the first part of the poem, the narrator expresses his desire for eternal unity with the divine as a logical foregone conclusion. As he describes his eternal bond, he sets up a parallel argument based on logical inference: He presents his passion as a fact of his life's first stage: "So was it when my life began"; a reality of the second: "So is it now I am a man," and a logical extension of the evidence in the third: "So be it when I shall grow old . . . ." However, eternity is not bound by space or time, and the linear argument split into temporal stages leads not to eternal life but rather to death "Or let me die!" So ironically, in his desperate longing to see his rainbow experience as indicative of his connection to the divine, his prideful certainty separates him from the universal spirit.