In this poem, Wordsworth expresses the feeling that his whole life is bound together by his love and respect for 'Nature' i.e. the world of the countryside that is now affected by the action of men. Wordsworth's heart is filled with an overwhelming joy whenever he sees the beautiful rainbow shining in the sky. He felt the joy of seeing the rainbow when he was a child , just as he does now. He even prays that it will be the same when he grows old even until the day he lays down on his death-bed. If his heart is not likely to feel the same joy in his old age whenever he sees the rainbow in the sky, then his wish is to let him die now before growing old.
Every person is first a child, then a man, so that the character of man grows out of the character of the character of the child., as a son receives his life from his father. The 'natural piety' has two meanings and Wordsworth probably intends both at once: (i) The respect and love which a child should have for his parents; (ii) Respect and love for Nature.
Thus Wordsworth's days are bound together because (i) he respects his childhood (the father of his manhood); (ii) he respects and loves the rainbow, which is one of the beauties of Nature, through all his life.