It is very useful for a lot of things. One way that it is useful is to calculate functions.
For example, how do you calculate \sin(1) (1 radians, not 1 degrees)?? You can plug it in your calculator, sure. But how did your calculator found the answer to the problem? Or how would you do this without a calculator?? This problem becomes easy once you know about series. Then you know that
\sin(1)=1-\frac{1^3}{3!}+\frac{1^5}{5!}+...
This is an infinite series, so you can't find the exact sum. However, if you take the first 3 or 4 terms then you already got a good approximation. This is one very efficient way to calculate function values.