A transformer is a device that transfers electrical energy from one circuit to another by electromagnetic induction (transformer action).
The electrical energy is always transferred without a change in frequency, but may involve changes in magnitudes of voltage and current.
Because a transformer works on the principle of electromagnetic induction, it must be used with an input source voltage that varies in amplitude.
Soft irons are ferromagnetic materials made of iron which can be magnetized and demagnetized easily. This is an advantage in transformers because in transformers, we need to constantly vary magnetism of the core.
This is important because without the change of magnetism of the core, there wouldn't be any voltage induced in the second circuit (the output)!
Hence, using a soft iron would allow the magnetism of the core to be changed easily, lessening the amount of energy lost and increasing the efficiency of the transformer.