Hysteresis is a measurement of an electrical component's change in performance as a result of continued operation. When a component is operated for the first time (for example, a temperature sensor reading temperature from cool to warm), it will follow a particular curve. When you then move the system in the opposite direction (say, change the temperature back to cool), the component will follow a similar curve back to its original state, but slightly displaced from the original curve, like so:

image from Wikipedia

A component's hysteresis is a measurement of its electromagnetic elasticity, in a manner of speaking. Think of it this way: When you run a magnet over a metal screwdriver, it becomes magnetized because of the efffect of the magnetic field. After a little time, though, the screwdriver demagnetizes. It returns to its original state, but not immediately. Kind of like a piece of elastic foam after being pressed on, it slowly returns to its original state.

Other electrical components react similarly to magnetic fields. They get temporarily magnetized, and this affects their performance. In sensors, hysteresis can lead to a sensor giving a different set of readings over time as its environmental conditions change back and forth (oscillate).

Thanks to Robert Faludi for this excellent link on hysteresis. Wikipedia has a good definition too.