It's a stanza from a poem by William Wordsworth:
MY heart leaps up when I behold
A rainbow in the sky:
So was it when my life began,
So is it now I am a man,
So be it when I shall grow old
Or let me die!
The child is father of the man:
And I could wish my days to be
Bound each to each by natural piety
This could be expanded in many dimensions. For instance:
This expression means that our psychology established during childhood, all our positive and negative traits are established when we are young. Traits and habits acquired during childhood remains with us lifetime. In this way, childhood got precedence our manhood and child leads the man in later life.
Another dimension:
Once Abraham Lincoln said:
"A child is a person who is going to carry on what you have started. He is going to sit where you are sitting, and when you are gone, attend to those things which you think are important. You may adopt all the policies you please, but how they are carried out depends on him. He will assume control of your cities, states and nations. He is going to move in and take over your churches, schools, universities, and corporations. All your books are going to be judged, praised or condemned by him. The fate of humanity is in his hands."
In this way, a child as judge of man's action may be termed as "The child is father of the man".