Why seizures spontaneously terminate remains an unanswered fundamental question of epileptology. Here we present evidence that seizures self-terminate via a discontinuous critical transition or bifurcation. We show that human brain electrical activity at various spatial scales exhibits common dynamical signatures of an impending critical transition--slowing, increased correlation, and flickering--in the approach to seizure termination. In contrast, prolonged seizures (status epilepticus) repeatedly approach, but do not cross, the critical transition. To support these results, we implement a computational model that demonstrates that alternative stable attractors, representing the ictal and postictal states, emulate the observed dynamics. These results suggest that self-terminating seizures end through a common dynamical mechanism. This description constrains the specific biophysical mechanisms underlying seizure termination, suggests a dynamical understanding of status epilepticus, and demonstrates an accessible system for studying critical transitions in nature.