The term "successions" refers to the body of law concerning the distribution of a person's property after he has died. Depending on the value of the property, the type of property, the debts of the decedent and some other factors, the process may be very simple or it may be very complicated.
An individual case will usually be referred to as the "Succession of John Doe" or simply "the succession." For ease of reference, attorneys will often refer to "the succession" as if it is a separate entity, for example they may refer to "rights belonging to the succession" or "debts of the succession." In reality, the succession is not a separate entity.
If an individual executed a valid testament, he is said to have died testate. If he had not executed a testament, if he had revoked his testament before he died, or if a testament is declared invalid by a court of law, he is said to have died intestate.