A terrorist reactor would be a reactor used for terrorist purposes. Imagine something like the infamous demon core, but set off in a populated area.
Prompt criticality is when a nuclear reactor is critical on prompt neutrons alone. This is to be avoided (in most cases) at all costs, as the doubling time of neutrons becomes very fast, a small fraction of a second. In a normally operating reactor, the core is subcritical on prompt neutrons, but critical on prompt + delayed neutrons. Delayed neutrons are emitted after the beta decay of certain fission products, and this slows the doubling of the neutron population enough that feedback control can keep the reactor's power steady.
