"terminal or digital member of the hand" (in a restricted sense not including the thumb), Old English finger, fingor "finger," from Proto-Germanic *fingraz (source also of Old Saxon fingar, Old Frisian finger, Old Norse fingr, Dutch vinger, German Finger, Gothic figgrs "finger"), with no cognates outside Germanic; perhaps ultimately from PIE root *penkwe- "five."
As a unit of measure for liquor and gunshot (late Old English) it represents the breadth of a finger, about three-quarters of an inch. They generally are numbered from the thumb outward, and named index finger, fool's finger, leech- or physic-finger, and ear-finger.
early 15c., "to touch or point to with the finger" (but see fingering (n.1) from late 14c.), from finger (n.). Sense of "play upon a musical instrument" is from 1510s. Meaning "touch or take thievishly" is from 1520s. The meaning "identify a criminal" is underworld slang first recorded 1930. Related: Fingered; fingering. Compare Dutch vingeren, German fingern, Swedish fingra, all from their respective nouns.