Normalization purpose in signal processing
Normalization is basically bringing the two signals to the same range or a predefined range. A typical example of a predefined range is the statistical perception of the normalization, which is transforming the signal so that its mean is $0$ and standard deviation is $1$. After such transform the canonical form is obtained. In layman's terms, such the operation consists of subtracting the minimum value and dividing by the range (difference between the maximum and minimum values).

Transforming all signals to such canonical form eases and robustifies the process of comparisons as well as serving too different needs such as visualization, and analysis. If we are to speak in terms of image normalization the effect would be the following: 

Un-normalized:



Normalized:



Note that, the distinction between the colors is clearer and more apparent.