When a person dies it is usually necessary for someone to administer the estate (the property) of the deceased person. The power to administer an estate is granted by the Supreme Courts of each state and territory.
Probate is the grant the court makes where there is a Will naming an executor. In other cases the court grants letters of administration. That may be because there is no Will, or no surviving executor or where administration is required for special purposes.
In order to obtain a grant the executor, or a person entitled to obtain letters of administration must apply to the court. Due to the particular and sometimes complicated requirements of the courts, a grant is almost always prepared through a lawyer.
Sometimes a grant is not required. If the estate is small and there is no dispute then often a grant will not be necessary, but some types of assets (such as land in most states) require a grant irrespective of the size of the estate.