The word exempt means to approve, to free oneself from something. The exemption is, precisely, freedom from a fault or a charge specifically applied to one. While the term can be applied to a myriad of situations and circumstances, it is primarily related to the situation of passing an exam at the academic level. The terms absolve, approve, and exonerate are synonyms of this word. It is also common to find it in the judicial sphere when referring to the punishment or sanction from which a person suspected of some type of crime was released.
The exemption is a concept that arises mainly in the judicial or prison world. Thus, this concept implies that a person suspected of a crime or offense is released from charges and exempted from receiving this or that punishment. At the same time, the exemption can mean freeing oneself from position or responsibilities with respect to a task to be carried out that does not imply a punishment but a certain effort. Thus, that one person exempts another from washing dishes would represent the opportunity that the exempted person does not have to carry out that activity.
Another very common use that is given to this word is the one that happens in the academic field when a person refers to passing an exam or not having to take it because they have passed the subject in a previous instance (which is commonly referred to as called promoting a subject). This meaning of the term is also related to the idea of freeing oneself from something since it assumes that the student gets closer to achieving the title by having fewer and fewer subjects to pass. The exemption can be given not only in final exams but it can also be given in any type of activity that represents the need to pass something.