The ancient Romans used a system of weights and measures based on units divided into 12 parts. The Latin uncia (from unus, meaning “one”), meaning “a 12th part,” designated the 12th part of a foot. From this is derived Old English ince or ynce and modern English inch.
Inch is one of the few units of measure that we have turned into a verb, in this case meaning “to move or progress very slowly” (as in “they inched toward a resolution”).
Apparently you can inch even when you’re using the metric system:
One of the more intriguing cultural phenomena of the last decade was the wristwatch renaissance. ... They inched toward 50 millimeters in diameter; they flaunted diamond bezels, tourbillion movements and complications galore; ...
— David Colman, The New York Times, 3 Dec. 2009