Short answers, pulled from the story.
An ecological threshold is the point at which a relatively small change or disturbance causes rapid change in an ecosystem. It matters because once crossed, the ecosystem may no longer be able to return to its prior state through its own resilience, making some thresholds effectively irreversible.
A point-type threshold involves an abrupt change at a specific moment, while a zone-type threshold involves a gradual shift or transition from one ecosystem state to another. Zone-type thresholds can be harder to detect because there is no single obvious moment of crossing.
Hysteresis refers to the dependence of a system's current state on the history of that state. In ecology, it means the path back from an altered ecosystem to its original condition can be drastically different from the path that led to the alteration, even when the change is not fully irreversible.
The thresholds database maintained by the Resilience Alliance and Santa Fe Institute includes over one hundred examples. Among the well-documented cases is clear lakes turning into turbid ones.
Panarchy views coupled human-natural systems as a cross-scale set of adaptive cycles across time and space. Sudden shifts in ecosystem state caused by threshold crossings can alter human understanding of management needs, which in turn changes the institutions that carry out management, feeding back into ecosystem change.
One key approach is processing time-series data believed to display a state shift, looking for identifiable jumps in the data. Methods have been developed specifically to enhance and localize these jumps in ecological records, though the non-linear nature of threshold responses makes early detection difficult.