Explain to me the secrets of Calculus

I will not take a Calculus class, but I know it contains a multitude of mind opening secrets, creating a sort of enlightenment wherein your perspective of the world and everything you know changes, but like a psychedelic drug, you can never describe it unless you make someone else go through it.  I refuse to go through the experience, but try to explain to me, a mere mortal, what these mind opening secrets and changed perceptions are.

I just want to know what it means when people say that anyone relying on math before calculus lacks understanding of math, and that their whole perception of math changes after calculus, until everything fits together in a way that it never did before, but only after you've been through Calculus (I ask if the basics of Calculus could be taught at Algebra, or at least an overview, and am told no, you have to get there to understand it first).  What was your perspective and understanding of mathematics prior to Calculus?