Step 1: Decode the Greek roots: $prosopon$ means face and $agnosia$ means loss of knowing. Put together, the word names a specific recognition failure for faces.
Step 2: A patient with prosopagnosia can see a face perfectly well but cannot match it to a known identity - even close relatives or their own reflection may seem unfamiliar. The lesion classically involves the fusiform face area in the ventral occipitotemporal cortex.
Step 3: Sort it from the confusables. Lack of awareness of one's own illness is anosognosia; inability to name or recognize objects is object agnosia; a drop in arousal is impairment of consciousness. Each maps to a different option, leaving 'difficulty in identifying known faces' as the unique match.
Step 4: Therefore prosopagnosia equals the selective inability to recognize familiar faces. \[\boxed{\text{Difficulty in identifying known faces}}\]