A few days ago, I honestly could not tell you the answer to the question "What is Calculus?"
Yes, I did take calculus (even did well on the AP exam) but it's been a long time (we're talking decades not years here) since I did anything involving calculus. Yes, I could take a simple derivative but, frankly, I just didn't remember much more than that.
However, a friend of mine (who spent several years as an electrical engineer before becoming an AP calculus teacher) and I started a new site dedicated to Calculus and higher math. To clarify our roles, he brings the calculus to the table and I bring the 'make it a web page.' I hope that this site will become a useful resource for any calculus student and teacher!
Anyway, I will not paraphrase the whole page, but if you want to know "What Calculus is", then simply visit this page. Trust me, if I got it, so will you.