Series in calculus are important for many reasons. One of them is the ability to differentiate or integrate a series that represents a function much easier than the function itself.
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Calculus was invented to solve physics problems, so the importance of studying calculus is to solve physics problems.
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Hence the reason for why it is called Vector Calculus, Vector Calc. is simply an expansion in the calculus subject are in math. It deals with Taylor's Formula (in calc 2 you learn the taylor polynomial and the taylor series), theorems from Green, Gauss, and Stokes, and much more.
Its importance is tremendous - it has many different applications. Some of the applications include calculation of area, of volume, moment of inertia, of work, and many more.