The phrase "cut to the quick" is an idiom that can be interpreted in a couple of different ways. Most of the time, the idiom is used to explain that someone has been badly hurt, usually in an emotional context rather than a physical one. Other times, however, to "cut to the quick" means to get to the root or the main point of an issue. In both cases, the main idea of the idiom is that the outer covering of something has been cut through to get to the inner, important issue, which may be painful when dealing with emotions.
The word "quick" sometimes describes living tissue, and is frequently used to refer to the nail beds of the fingers and toes. When an individual cuts his or her nails too short, down into the quick of the nail bed, it can be very painful because the normal protective covering has been removed. This common occurrence is the physical basis for the metaphor of being emotionally "cut to the quick," with painful, sensitive emotions suddenly exposed like a nail bed whose protective fingernail has been cut too short.
This idiom can be used to refer both to the person doing the hurting or to the person being hurt. It would be correct to say that a hurtful person cut his friend to the quick with a mean comment. It is also correct to say that the friend has been cut to the quick by the mean comment. In this instance, the friend's protective emotional barrier has been cut through, to expose the painful feelings underneath. Since the most meaningful, important feelings are the ones that have been deeply hurt, the friend who has been cut to the quick is not likely to recover and forgive the insult anytime soon.
Similarly, getting to the main idea of an issue is also considered cutting to the quick. In this definition, too, the outer layer of unimportant things has been cut through in order to address the core of the situation. For example, a nervous business partner might wish to stall for time by using small talk, while the other partner attempts to cut to the quick of the conversation, sweeping aside the trivial issues to discuss the more important matters. This form of the idiom is used less frequently than the emotional one, though the main idea of both is the same.