What are Limits in Calculus?

Back when I was taking my introductory calculus courses, one of the first topics that we covered was a section on limits and rates of change.  To a math student, "rate of change" kind of makes some sense.  It sounds like a math concept that explains how fast something is changing.  It's a fairly intuitive concept, and we will eventually see that it is a very important concept as well!  On the