In general, the input in these kinds of output-vs-input curves is the current that drives the neuron whose output we are measuring. In the case of the Hopfield model, where we interpret the state variable sigma as a spike, the input current roughly corresponds to the sum of all weighted incoming spikes, i.e.: SUM{ w_ij sigma_j }. For a more detailed explanation of how inhibitory population 2 can be constructed in this way, see section 17.3.2 in the text book.
Regarding inhibitory population 1, as is also explained in section 17.3.2, the output-input curve has a switch-like behavior and turns on to suppress the excitatory neurons whenever their total activity ( SUM sigma_i ) surpasses the desired activity ( a*N ).
