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Calculus is a branch of mathematics, developed independently by Newton and Leibniz and formalized in the 19th century by various mathematicians, that revolutionized human [understanding] of the world.  [Mathematically], it allows us to talk about instantaneous rates of change and areas under arbitrary curves.  Doesn't sound important?  When does anyone use this?  Differential equations, which express the relation between two quantities in terms of how they change with respect to one another, allow us to model situations in which we cannot explicitly find the [relationship] between quantities.  This concept can be applied to model situations in physics, engineering, chemistry (how does this reaction progress?), physiology (how does a muscle contract?)...just about any science, as well as economics, sociology (how do new ideas spread?), and more.  If you want to understand the world today, you need to understand calculus.  Statistics too...but that's another story.

Calculus is not some super-hard subject that only the most brilliant can handle.  If you have a good teacher who explains things precisely, you can learn calculus.  (Finding such a teacher, [unfortunately], can be the hard part.)

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