When an iron piece is magnetized in a strong external field, the closed molecular chains break down and all molecules begin to align themselves in the direction of the external magnetic field.
As the magnetizing field is increased, more molecular magnets align in the given orientation.
Thus, the magnetic strength of the iron piece increases with the increase in the strength of the external magnetic field.
When all molecules of the iron piece have aligned themselves there is no further increase in its magnetic strength even if the strength of the external magnetic field is increased.