What is representation in optical character recognition?
The representation step is before the feature extraction step for exactly the reasons that they state. 

If you take the full image representation and go right to feature extraction, you have much more data to extract features from (added complexity) and the features you do extract will be much more noisy. This is why one at least reduces the representation to grey level (as the authors suggest). 

Feature extraction is choosing properties of the image which you will then perform recognition on. It is important to already have thrown out unimportant details of the image before doing this. That is why the authors, and people in general, reduce to a proper representation before performing feature extraction.