Hysteresis
Definition
When a material 'remembers' its magnetic past — magnetize iron and some magnetism lingers after you remove the field.
Technical definition
The B–H curve traces a loop whose area is the energy lost per cycle as heat. Remanence (leftover B) and coercivity (field needed to erase it) characterize the material.
Example
Transformer cores use low-hysteresis silicon steel — a wide loop would waste energy as heat 50 or 60 times every second.
Common confusion
Hysteresis is not mere 'lag'. It is path dependence: the state depends on history, not just the present field — which is exactly why it makes good permanent magnets and memory.