"Plant" is a legacy term referring to the device or system acting on the state you're trying to control. Sticking with thermostats, the plant is the heating element.
A straightforward way to think of hysteresis is that the output depends on the history of the input. A simple example of hysteresis in a temperature controller would be to turn off heat if the temperature rises above threshold A, but only turn on heat if the temperature falls below threshold B.
"These controllers may be realized in terms of any element that provides hysteresis" -- This is indeed awkward phrasing, since it could be read as though the property of hysteresis is fundamental to create a bang-bang controller. In fact, using hysteresis is "just" a best practice. Strictly speaking, you could make a hot water heater that turns heat on and off based on a single hard temperature threshold as measured by a thermometer, and it would work. However, any noise in the system will make the output jittery and cause unnecessary cycles. Having a "heat off" threshold higher than the "heat on" threshold makes for smoother transitions.
So who's the "typical reader"? Web designers? Startup founders?
Bonus ironic jab/useful information combo: https://simple.wikipedia.org/wiki/Hysteresis
You mean for Hacker News, or Wikipedia? There's actually a Wikipedia article about that (https://en.wikipedia.org/wiki/Wikipedia:Readers_first), but a good rule of thumb is that articles should be written for the layperson except where that would impact accuracy. I think Styrophone's explanations above demonstrate that this particular article could be a lot clearer without sacrificing accuracy.
Specialities mangle language. It's just the way the world is.