In a transformer or inductor, some of the power that would ideally be transferred through the device is lost in the core, resulting in heat and sometimes noise. There are various reasons for such losses, the primary ones being:
When the magnetic field through the core changes, the magnetization of the core material changes by expansion and contraction of the tiny magnetic domains it is composed of, due to movement of the domain walls. This process causes losses, because the domain walls get "snagged" on defects in the crystal structure and then "snap" past them, dissipating energy as heat. This is called hysteresis loss. It can be seen in the graph of the B field versus the H field for the material, which has the form of a closed loop. The amount of energy lost in the material in one cycle of the applied field is proportional to the area inside the hysteresis loop. Hysteresis loss increases with higher frequencies as more cycles are undergone per unit time.
Eddy current loss
The induction of eddy currents within the core causes a resistive loss. The higher the resistance of the core material the lower the loss. Lamination of the core material can reduce eddy current loss, as can making the core of a magnetic material nonconductive, like ferrite.