Specific reading is the reading that an indefinite noun phrase has when there is a particular referent of that noun phrase. In the sentence John seeks a unicorn, a unicorn has a specific reading when there is a particular unicorn that John is looking for. This reading entails the existence of unicorns in the domain of discourse. A unicorn has a nonspecific reading when John is looking for an arbitrary unicorn. This does not entail the existence of unicorns. The specificity-contrast is often analyzed in terms of the relative scope of the indefinite with respect to an opaque context. The specific reading, then, corresponds with the wide scope (or de re) reading, while the nonspecific reading corresponds with the narrow scope (or de dicto) reading.
Utrecht Lexicon of Linguistics