Extract most informative parts of text from documents
What you're describing is often achieved using a simple combination of TF-IDF and extractive summarization.

In a nutshell, TF-IDF tells you the relative importance of each word in each document, in comparison to the rest of your corpus. At this point, you have a score for each word in each document approximating its "importance." Then you can use these individual word scores to compute a composite score for each sentence by summing the scores of each word in each sentence. Finally, simply take the top-N scoring sentences from each document as its summary.

Earlier this year, I put together an iPython Notebook that culminates with an implementation of this in Python using NLTK and Scikit-learn: A Smattering of NLP in Python.