The discussion is quite abstract - perhaps that's why it's difficult to grasp. As I understand it, the climate can be regarded as a dynamical system currently existing at a stable equilibrium. I.e. small perturbations to the state tend to be damped. If there's a massive volcanic event, we will have a few cold years, but the climate will return to something familiar.

It's stable, as when you add up all the positive and negative feedback effects, the result is negative. The most important negative comes from the thermal radiation of the Earth into space, which increases with increasing temperature, resulting in more cooling. Methane in Siberian ice is a hypothesised positive feedback effect: higher temperature => more methane => more warming.

If all these effects ever add up to more than 0 (the "tipping point"), the system will no longer be stable, and will travel around until it finds another stable equilibrium. The actual consequences of this are nowhere stated because they are completely unknown. But we're not talking about measuring sea-levels, we're talking a completely different climate (e.g. Venus).