A paradox, according to the eNotes Guide to Literary Terms, is "a statement that is apparently self-contradictory or absurd but really contains a possible truth. Sometimes the term is applied to a self-contradictory false proposition."
In his poem "The Rainbow," Wordsworth talks about feeling joy upon seeing a rainbow and that this feeling was the same when he was a child as it is now when he is a man. He hopes that he will still feel that way when he is an old man.
Then the speaker says something odd: "The Child is father of the Man." We know he can't mean that literally because a child cannot be a father to a grown man; it is the other way around. That is the paradox. The statement makes no sense by itself. However, when we put it in the context of what we have already read, that he had great joy in rainbows as a child and that the joy has continued into adulthood, then we can realize that he means that his childhood experiences have made him what he is now as a man. In a sense, the child that he was has given birth to the man that he is; therefore, the child is the father of the man.
I hope this helps you!
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 childhood experiences become the foundation for all adult experiences. It is the childhood of a person which shapes and thus 'fathers' or creates the mature adult. So, "The Child Is the Father of the Man."
This is the truth behind the paradox.