Wordsworth begins his poem by stating how his "heart leaps up when I behold/A rainbow in the sky", and how it did this when he was a child too, and it will when he is old. So what he means by the quote "The Child is father of the Man" is simply that as a child, he felt the same awe and respect for nature that he does as a man, and how the child, in its simplicity and innocence, is often wiser than the man, and can teach the man a few things, like a father.
A major theme of a lot of Worsdworth's poetry is the beauty of childhood-he thinks that "Heaven lies about us in our infancy!", that we are closer to wisdom and God when a child than when an adult. As an adult, we don't still have that awe and reverence that children do, "The things which I have seen I now can see no more" and the world ruins us. So Wordsworth feels that the child, having more wisdom and being closer to God, can be the greater teacher, or father, to the man. I provided links to another Wordsworth poem that follows this theme also ("Ode: Intimations of Immortality").
First, it's worth mentioning that Wordsowrth and other romantic writers liked beauty and innocence, besides William Blake sees that children are the only human being on earth. Wordsowrth in this poem describes his feelings when he was a child, and how he was connected to nature . These feelings of beauty and innocence are the same feeling he has when he grows up . In other words, the child's feelings are controlling him whem he becomes a grown up man; thus, the child in the father of the man .
notable that father could mean parents. Wordsworth used to call nature as mother nature, and he wrote a group of poems called Lucy poems in which he describes a little child, the poet himself, and his feelings . This child is considered as a symbol of nature, so the realtionship between him and the man is the same to the relationship between a mother presented in nature and a child .