This tool at Smith’s Tavern is an apple butter paddle-stirrer.
Anything that touched apples had to be made of wood. Even a nail would “risk spoiling the flavor” or “quicken a souring” [even though Smith’s Tavern’s version has metal screws]. So heavy treen-ware (appliances and tools made of wood) were necessary in the apple industry.
Apple butter is a highly concentrated form of apple sauce produced by long, slow cooking of apples with cider or water to a point where the sugar in the apples caramelizes, turning the apple butter a deep brown. The concentration of sugar gives apple butter a much longer shelf life as a preserve than apple sauce.
The paddle was an important part of the apple butter making process. The butter was cooked in copper kettles over an open flame. The paddle was used to continuously stir the butter to prevent it from sticking to the bottom and burning.
The long handle allowed the stirrer to stand away from the heat. The holes in the bottom ensured that the apple pulp was comprehensively agitated with each stir of the paddle.
Reference: A Museum of Early American Tools, by Eric Sloane, page #46-47 and http://www.sa1969.com/apple-butter-paddle-320-p1192.html