This inversion of the natural order of things means that by studying the character of the child we can tell what sort of a man he is going to be. As Milton wrote in Paradise Regained: The childhood shows the man, as morning shows the day.
The source of the proverb is a short poem by 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 the father of the Man:
And I could wish my days to be
Bound each to each by natural piety.