How would you describe calculus in simple terms? I keep hearing about this weird type of math called calculus. I only have experience with geometry and algebra. Can you try to explain what it is to me?
There came a time in mathematics when people encountered situations where they had to deal with really, really, really small things.

Not just small like 0.01; but small as in infinitesimally small.  Think of "the smallest positive number that is still greater than zero" and you'll realize what sort of problems mathematicians began encountering.

Soon, this problem became more than just theoretical or abstract.  It became very, very real.

For example, velocity.  We know that average velocity is the change in position per change in time (i.e., 5 miles per hour).  But what about velocity at a point in time?  What does it mean to be going 5 mph at this moment?

One solution someone came up with was to say "it's the change in position divided by the change in time, where the change in time is an infinitesimally small amount of time".  But how would you handle/calculate that?

Another problem came about trying to find the area under a curve.  The current accepted solution was to divide the curve into rectangles, and add together the area of the rectangles.  However, in order to find the exact area under the curve, you'd need to divide it into rectangles that were infinitesimally tiny, and, therefore, add up an infinite amount of tiny rectangles -- to something that was finite (area).

Calculus came about as the system of math dedicated to studying these infinitesimally small changes.  In fact, I do believe some people describe calculus as "the study of continuous changes".
This is the simplest explanation. 

http://www.math-prof.com/Calculus_1/Calc_Ch_01.asp

ie...its simply a way of dealing with an equation where the denominator has become 0. Instead of leaving it as insoluble...you have a method of proceeding.