The word Calculus comes from Latin meaning "small stone",
Differential Calculus cuts something into small pieces to find how it changes.
Integral Calculus joins (integrates) the small pieces together to find how much there is.
Read Introduction to Calculus or "how fast right now?"
Limits are all about approaching. Sometimes you can't work something out directly, but you can see what it should be as you get closer and closer!
Derivatives (Differential Calculus)
The Derivative is the "rate of change" or slope of a function.
Taylor Series (uses derivatives)
Integration (Integral Calculus)
Integration can be used to find areas, volumes, central points and many useful things.
In our world things change, and describing how they change often ends up as a Differential Equation: an equation with a function and one or more of its derivatives:
If you want more Calculus topics covered, let me know which ones.