Letters of Administration in Victoria is similar to the Grant of Probate because it establishes a person, or people, who are entitled to act on the behalf of the estate - calling in the estate assets, paying the liabilities and transferring the residue to the estate beneficiaries.
The main difference is the existence of a will.
If your loved one left a valid will, in most cases you should apply for a Grant of Probate in Victoria. If they did not leave a will (i.e. they died “intestate”) then the Courts determine who will be the estate representative, the “administrator”, by looking to the Administration and Probate Act 1958. The Letters of Administration application proves to the Court, via the production of documentary and affidavit evidence, the family tree of the deceased.