Manumission is the act of freeing a slave, done at the will of the owner. It can be done very formally and publicly but is often done with little publicity and many tears. Within BDSM, the term is rarely used although the act is about as common as any other relationship breakdown.
Manumission is a tenuous process at best. Most slaves come to love their Master or Mistress deeply, even if the relationship did not start out based on love. In addition to the emotional pain typical in any relationship breakdown, many freed slaves feel extremely bewildered and lost. While they can normally cope better than most people in understanding and manipulating the bureaucracies that make up every day modern life, they are not used to making the decisions in their personal life and rarely have an inclination to do so. Most slaves are very competent people so will cope well on their own but simply don't want to: they have a deep-seated need to belong. This means that, once the emotional issues are cleared, they usually will seek out another owner, often one very much like their last, even though there was clearly some reason why the last relationship didn't work.
Many slaves who have experienced manumission do not want to go through it again and, once owned again, would far rather be traded or given to another owner of suitable gender so long as they can feel the new owner will take proper care of them. This is not universal, however and most slaves who have not experienced manumission think they would prefer to be freed rather than passed to a different owner.
The term is Middle English and is derived from the Latin manumittere (to send from one's hand or control, from manus, hand, and mittere, to send).