The phrase "equilibrium state" refers to a state or condition where different forces or factors in a system are balanced or stable. It means that everything is in a state of rest or harmony, without any significant changes occurring. Full definition
It can only be a result of a changing equilibrium state of the carbon cycle. (wattsupwiththat.com)
What is somewhat unsettling here is the lack of apparent negative feedbacks that would lead to a new stable equilibrium state. (realclimate.org)
Over geological time ie the hundreds of millions of years it must balance out but with a chemical potential of components in a far from equilibrium state. (realclimate.org)