Let's say you have the following greyscale image:
$A = \begin{pmatrix} 255 & 50 & 255\ 0 & 50 & 50 \end{pmatrix}$
Histogram
Now the histogram is a function $H: [0,255] \rightarrow \mathbb{N}_0$.
The histogram of $A$ is
$H(x) := \begin{cases} 1 &\text{, if } x = 0\ 3 &\text{, if } x = 50\ 2 &\text{, if } x = 255 \end{cases}$
Accumulated histogram
The accumulated histogram $H_\alpha: [0,255] \rightarrow \mathbb{N}_0$ is defined as
$H_\alpha(x) := \sum_{i=0}^x H(i)$
This means, in the given example you get
$H_\alpha(x) := \begin{cases} 1 &\text{, if } x < 50\ 4 &\text{, if } 50 \leq x < 255\ 6 &\text{, if } x = 255 \end{cases}$
Normalized histogram
The normalized histogram is defined as $H_n(x) := \mathrm{round}(\frac{255}{w \cdot h} \cdot H_\alpha(x))$ where $w$ is the width of the image and $h$ is the height of the image.
In our example it's:
$H_n(x) := \begin{cases} 43 &\text{, if } x < 50\ 170 &\text{, if } 50 \leq x < 255\ 255 &\text{, if } x = 255 \end{cases}$
So the resulting image is
$A = \begin{pmatrix} 255 & 170 & 255\ 43 & 170 & 170 \end{pmatrix}$