The straw that breaks the camel's back
In the early days of the IPCC, climatic tipping points were still among the more eccentric, extreme visions of the future that were of little concern to the mainstream. This has since changed. Tipping points have long since entered the mainstream of climate science and are therefore gradually becoming part of public discourse. The IPCC defines tipping points as the points at which irreversible changes in the climate system occur.
From a more formal mathematical point of view, climatic tipping points are bifurcations combined with hysteresis in a dynamic system. We won't go into details, but hysteresis is an important concept to understand the principle of tipping points, so we will briefly discuss it: In simple terms, hysteresis refers to the dependence of a system state on its history.
Let's imagine a 32° steep, snowy slope. No avalanche has yet occurred on this slope (system state 1: slope intact). Now it is snowing half a meter. Whether the weight of the new snow will trigger a spontaneous avalanche depends on the snowpack structure, i.e. the previous history of the system. If the old snowpack is favorable, nothing may happen. However, if the situation is unfavorable, for example because the surface layer is weak, an avalanche will occur. The system state has thus changed abruptly and irreversibly (system state 2: slope has gone down)!
So, hysteresis: Depending on the previous history, small, gradual changes in a variable (e.g. fresh snow) cause small, easily predictable changes in the overall system (snow depth increases), or a fundamental change in the system state (avalanche goes down). When exactly the latter occurs is subject to some uncertainty with avalanches as with the climate - we know roughly how the whole thing works and when it starts to become critical, but at what moment exactly the system tips over (at how many centimetres of fresh snow does the weak layer break?) is not so easy to predict.