The term normalization has a different meaning depending on the context. This is mainly for my own understanding, to get the definitions clear in my head. But I hope that others find this useful.
In the context of Relational Databases normalization mean to organize data in a way that eliminates redundant data (e.g. data that is stored in multiple fields) and ensuring that only data that is related is stored in the same table.
In statistics, normalization can have a variety of meanings. The most common definition is adjusting the values so that it can be measured on a different scale. For example, dividing a histogram by the number of entries changes the scale from frequencies to probabilities (changing it from a histogram to a probability mass function).