Self-harm, also known as self-injury, self-inflicted violence, self-injurious behavior, or self-mutilation, can be defined as the deliberate, direct injury of one's own body that causes tissue damage or leave marks for more than a few minutes and that is done in order to deal with an overwhelming or distressing situation.
It's important to remember that, even though it may not be apparent to an outside observer, self-injury is serving a function for the person who does it. Figuring out what functions it serves and helping someone learn other ways to get those needs met is essential to helping people who self-harm.
Some of the reasons self-injurers have given for their acts include:
Affect modulation (distraction from emotional pain, ending feelings of numbness, lessening a desire to suicide, calming overwhelming/intense feelings)
Maintaining control and distracting the self from painful thoughts or memories
Self-punishment (either because they believe they deserve punishment for either having good feelings or being an "evil" person or because they hope that self-punishment will avert worse punishment from some outside source
Expression of things that can't be put into words (displaying anger, showing the depth of emotional pain, shocking others, seeking support and help)
Expression of feelings for which they have no label -- this phenomenon, called alexithymia (literally no words feeling), is common in people who self-harm
See Osuch, Noll, & Putnam, Psychiatry 62 (Winter 99), pp: 334-345
Zlotnick et al, Comprehensive Psychiatry 37(1) pp:12-16.
People who self-injure often never developed healthy ways to feel and express emotion or to tolerate distress. Studies have shown that self-harm can put a person at a high level of physiological arousal back to a baseline state.
It's natural to want to help people who self-injure develop healthier ways of coping when they feel overwhelmed, but it's important not to let your discomfort with the concept of self-harm cause you to issue ultimatums, punish self-harming behavior, or threaten to leave if the person self-harms again. Ideally, you should set boundaries to keep yourself feeling safe while respecting the person's right to make his or her own decisions about how to deal with stress.