means The pale, silvery light cast by the moon at night — or, used as a verb, working a second job, typically secretly and after hours.

from A plain old English compound, joining 'moon' (Old English 'mōna,' a cousin of German 'Mond' and Latin 'mēnsis,' month — the moon was the ancient world's calendar) with 'light' (Old English 'lēoht'). The verb sense — taking on extra work in the dark — is far younger, an Americanism that grew from the older 'moonlighting,' which once meant nighttime mischief and illicit deeds carried out under cover of that forgiving glow.