Webster's Seventh New Collegiate Dictionary tells us:
a retardation of the effect when the forces acting upon a body are changed (as if from viscosity or internal friction); esp: a lagging in the values of resulting magnetization in a magnetic material (as iron) due to a changing magnetizing force. -hys-ter-et-ic adj
Hysteresis represent the history dependence of physical systems. If you push on something, it will yield: when you release, does it spring back completely? If it doesn't, it is exhibiting hysteresis, in some broad sense. The term is most commonly applied, as Webster implies, to magnetic materials: as the external field with the signal from the microphone is turned off, the little magnetic domains in the tape don't return to their original configuration (by design, otherwise your record of the music would disappear!) Hysteresis happens in lots of other systems: if you place a large force on your fork while cutting a tough piece of meat, it doesn't always return to its original shape: the shape of the fork depends on its history.
Hysteresis loops happen when you repeatedly wiggle the system back and forth (cycle the field up and down). The magnetization of a tape will ``lag behind'' as the field sweeps up and as it sweeps down. The memory in the tape is the magnetization remaining as the field is released to zero from a large value. In magnetic tapes, this lag is repeatable: the shape of the loop after the first cycle is roughly the same as it is after many cycles. (This is convenient for doing multiple recordings on the same tape.) This is not true of many other systems: forks, for example, after being bent back and forth many times, will actually become stiffer (``work hardening'') and then break. There is a class of metals (called shape memory alloys) that can be bent or stretched plastically large distances back and forth many times without work hardening: this superelastic behavior is only one property of these interesting materials.
Many hysteretic systems make screeching noises
as they respond to their external load (hence, the natural connection
Jim Sethna, firstname.lastname@example.org
Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).