What does $a$ mean in Taylor series formula? I'm trying to code the Taylor summation in MATLAB, being Taylor's formula the following:  

I've also seen $a$ denoted as $x_0$ in distinct bibliography.
Problem is that I'm not sure how should I evaluate or assign for $a$.
At lecture I studied the exponential Taylor's representation being: 
And I got to that same summation by evaluating $a$ as 0 but and I know that is meant to be McLaurin formula, but what's within evaluating with a different value or letting $a=x$?
What should I do in order to code properly Taylor summation for distinct functions?

Taylor series  approximates  given function at some point,in your case  if we have given  some function  $f(x)$ and we can't compute exact value of this function at point $x=a$, we  are trying to approximate  it using derivatives at given point $x=a$,so in short  this is a point where we  want to  compute  function value
