When a person dies, they usually leave behind various assets, debts and outstanding matters. The process of dealing with these issues is called estate administration.
Usually, the executor named in the will administers the estate. If there is no will, or the will did not appoint an executor who is willing and able to act, then it is usually the main beneficiary of the estate who will take on the role of the administrator and administer the estate.
Estate administration involves obtaining a grant of probate or letters of administration, calling in the assets, paying debts and then distributing the estate in accordance with the will. If there is no will, then the estate should be distributed in accordance with the law.