Basic calculus is about the study of functions. The two main divisions of calculus are differentiation and integration. Differentiation has to do with finding the tangent line to a function at any given point on the function. Integration has to do with finding the area under (or above) a curve.
Other topics covered in calculus include:
Differential equations
Approximations of functions (linear approximation, series, Taylor series)
Function analysis (Intermediate Value Theorem, Mean Value Theorem)