When reading information-dense work, such as papers , it is important to extract its interesting/useful concepts. In this case, a concept summary is a self-contained piece of text that shows a conclusion, its difficulties, methods, and hypothesis, not necessarily in that order.
One of the advantages of extracting concept summaries is that it allows for easy linking of notes . For example, it is possible that unrelated papers have common hypothesis, or methods. It can be that the difficulty on one is the the conclusion of another, etc.
Another advantage is that concept summaries can be augmented through building knowledge. The same concept can be tackled in two different works, and therefore their information can be combined. Using concept summaries is useful for preventing the natural siloing of information that would happen if notes where taken under a paper's title.