The top graph shows $f(x) = x(x-2)^2 + 1$ and the tangent line at $x=a$.
Recall that
$$ \text{Slope of the secant line between $a$ and $x$} \ =\ \frac{f(x)-f(a)}{x-a}.$$
Hence, for any $a$,
$$f'(a)\ =\ \text{Slope of tangent line at }a \ =\ \lim_{x \rightarrow a} \frac{f(x)-f(a)}{x-a}.$$
The value of $f'(a)$ for each $a$ is plotted on the bottom graph.
As $a$ changes, $f'(a)$ traces out a function.
Thus, $f'(x)$ as a function of $x$, where, given $x$, the value of $f'(x)$ is the slope of the tangent line to $f$ at $x$.