The old man mumbled to himself as if recalling the past.
Tips
memory
喃喃 is onomatopoeia for soft, continuous murmuring - say the syllables out loud and you hear the sound. 自语 = 'speaking to oneself'. The whole phrase is as acoustic as it is descriptive.
usage
Neutral, descriptive. Common in narrative writing to convey an inward or troubled state. The shorter 自言自语 is a near-synonym and more colloquial.