Hard and soft are term describing the magnetic properties of the material. In hard iron the domains do not shift back into their random positions when the external field is removed. In soft iron, the domains do shift back into their random positions when the external field is removed. To make permanent magnets a piece of hard iron is placed into a magnetic field. The domains align with the field, and they retain most of that alignment when the field is removed.
Soft iron is used as a core in electromagnets.
A wire is wound around an iron core. A current flowing through the wire coil produces its own magnetic field and magnetizes the iron. The magnetic field produced by the iron is much stronger than the field produced by the current in the coil. Typically an iron core magnifies the field by a factor of 100 to 1000. When the current in the coil is reduced to zero, the soft iron core looses its magnetization.