What does the phrase " the child is a parent to us all" mean?
This is a new phrase to me. It might have been helpful to have been told the context in which you encountered it.
My interpretation, based on many years of observing and working with and learning about and from children, is that there are times when we adults need to learn from the children around us. I think we could all take lessons from youngsters who are open to new experiences and are eager to learn by trying different activities. They are not inhibited by preconceived notions or prejudices and are ready to accept observations for what they are, without trying to read ulterior meanings or complications into them.
As parents, adults try to lead their children to situations that will teach the children what they should know and how they should act. I think your quote is saying that there are times when we should allow the child to be the parent, leading us in finding better, more open and honest ways to learn.