These days the term desistance is most often used in criminology and sociology to refer to someone who has ceased to commit crimes. While the term is often somewhat vague, the overtone is that the person changed their behavior with minimal, if any, formal intervention. That is, they did not go to prison, may not have gone to court, and may in fact never have been caught. While the term is often entangled with models of restorative justice, there is no necessary connection between the two.
Desistance models emphasize the important of community and personal growth in managing crime. While this sounds a bit nebulous -- and currently it certainly is nebulous -- it is empirically the case that things like integration into the community, marriage, employment, finding religion, and strong family ties all impact criminal behavior. Counseling or simply setting up conditions in the community to support cases of 'spontaneous desistance' can be effective and are generally cheaper than prison.
Somewhat controversially, another common use of the term is to refer to people who expressed gender confusion, and then stopped. Desistance is formally used in studies on gender dysphoria with no intent of causing offense, but it is clearly a hangover from when being transgender was viewed as a perversion needing correction. There is also some debate over what desistance means in this context; if before puberty a child says that they are not their assigned gender, and after puberty says never mind, I'm just gay, is that desistance? If a person moves from wanting gender reassignment treatments to being happy without medical interventions, but still identifies as non-binary, is that desistance? The growing acceptance of alternate gender identities has reduced the concern over desistance, but it is still a consideration in cases where medical interventions are requested.