something heard while sleeping
Refers to information or sounds perceived during sleep, often used in the idiom 寝耳に水 (a bolt from the blue).
The news came as a complete surprise.
It was such a bolt from the blue that I was speechless for a while.
Compound of 寝 (ne, 'sleep') and 耳 (mimi, 'ear'). The exact historical derivation is uncertain, but it literally means 'sleeping ear'.