Can somebody give me a good explanation on Euler's number?

Here is another link

http://www.askamathematician.com/2013/01/q-what-makes-natural-logarithms-natural-whats-so-special-about-the-number-e/

I don't pretend to understand this very well myself but one very important quality of e is that if you graph $$y=e^x$$ on the number plane then the gradient of the tangent to the curve at any point is also    $$e^x$$

In terms of calculus this means that if

$$\\y=e^x\;\;then\\
y'=e^x\quad too.$$

Also

This is a very important fact when dealing with continuous exponential growth and decay.

Here is another site

http://en.wikipedia.org/wiki/Exponential_function

Here you go, DB.......not too difficult to understand, I don't think.......

http://www.mathsisfun.com/numbers/e-eulers-number.html