All brain normal or pathological activities occur in one of the states of vigilance: wake, slow-wave sleep, or REM sleep. Neocortical seizures preferentially occur during slow-wave sleep. We provide a description of neuronal behavior and mechanisms mediating such a behavior within neocortex taking place in natural states of vigilance as well as during seizures pointing to similarities and differences exhibited during sleep and seizures. A concept of epileptic focus is described using a model of cortical undercut, because in that model, the borders of the focus are well defined. In this model, as in other models of acquired epilepsy, the main factor altering excitability is deafferentation, which upregulates neuronal excitability that promotes generation of seizures. Periods of disfacilitation recorded during slow-wave sleep further upregulate neuronal excitability. It appears that the state of neurons and neuronal network in the epileptic focus produced by deafferentation are such that seizures cannot be generated there. Instead, seizures always start around the perimeter of the undercut cortex. Therefore, we define these areas as the seizure focus. In this zone, neuronal connectivity and excitability are moderately enhanced, lowering the threshold for seizure generation.