What is an example of normalization (making the row unit norm)?
A very simple example is the use of relative frequency instead of absolute frequency, for instance in text classification: if the features represent the raw absolute frequency of every word, then large documents have higher values than small documents. In this case the learning algorithm won't be able to distinguish between a word used 10 times in a small 50 words document (so this word is important for the document) vs. the same word used 10 times but in a large 1000 words document (not very important for the document).
Using relative frequency instead (i.e. dividing by the size of the document) solves this problem. It's an example of row-wise normalization, there are many others.