This is a miter box, branded Craftsman, but I believe made by Millers Falls, who acquired the company that was the original manufacturer, Langdon Mitre Box Company, in 1907. Leander W. Langdon was the creator and patented (1, 2) his idea in 1864.
This site is devoted to Langdon miter boxes, and is pretty great.
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I wrote to the guy that runs that site, asking if he could identify this one and received this:
It looks to me like you have a post-WWII model 1124. It is a derivative of Goodell Pratt, which was bought up by Millers Falls Company during the Great Depression.
Craftsman and Millers Falls items are identical in all respects but for the label.
I’ll be sending him some pictures of mine for his site.
Here’s the manual for the 1124.