So, the population size of the plants [eaten by herbivores], and of these herbivores is steady cos their food supply has not changed, and hence the carnivores who eat these herbivores remain steady in number.
Other factors that could upset the equilibrium e.g. any flooding or heat wave, which might kill some animals, or conversely any drought or "ice age", respectively, that could do the same, are absent.
So "population sizes remain constant" i.e., the numbers of live members of various species does not change much, yeah?
I hope this sorts your issue!