Question 870605
This is from the definition of the derivative 


<img src="http://www.sciweavers.org/tex2img.php?eq=%5Clim_%7Bh%5Cto%200%7D%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D&bc=White&fc=Black&im=jpg&fs=18&ff=arev&edit=0" align="center" border="0" alt="\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}" width="231" height="65" />


where x = a. So instead of calculating f'(x), which is a general algebraic expression, you are calculating f'(a) which is a single number.



Geometrically, or graphically, f'(a) is the slope of the tangent line to f(x) at the point x = a on the function f(x). Put another way, we have some tangent line y = mx+b where m = f'(a) and the tangent line goes through the point (a, f(a)). 



Here is a good animation that shows what's going on.



<a href="http://math.bu.edu/people/tkohl/teaching/spring2013/secant.html">http://math.bu.edu/people/tkohl/teaching/spring2013/secant.html</a>


Visually, h is the horizontal distance from point P to Q. The secant line is going through points P,Q. 
As Q gets closer to P, that secant line is slowly becoming a tangent line. 
It is only a tangent line when P = Q since tangent lines only cross the function (locally) at one point.