Currently I'm reading [*Higher Engineering Math* by John Bird](http://books.google.com/books/about/Higher_engineering_mathematics.html?id=_JMa8uYbOGgC) and under exponential function he talks about obtaining the value of **$e$**.

He begins by saying 

>The value of **$e^x$** can be calculated to any required
degree of accuracy since it is defined in terms of the following power series:
$$e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots $$
> The series is said to converge upon substituting $x = 1$ which gives $e = 2.7183$ correct to 4 decimal places. 

My question is what is this "power series" and where did it come from?
How can one define **$e^x$** in terms of the above power series?