This weird-looking thing is a FootFitter Boot Stretcher. And if your feet are AT ALL wider than “medium,” you want one. (In fact, you want two, but you can get away with one.)
I finally broke down and bought one late last year and have now managed to rescue several pairs of shoes that were previously too painfully narrow to wear. Using it couldn’t be simpler: fill a spray bottle with 50% water/50% rubbing alcohol, spritz the inside of the shoe or boot you want to stretch, and insert device. Turn handle to stretch. (The black bobbles in the picture are inserted into the holes in the fitter to add extra stretchy to accommodate corresponding bumps on your own feet.)
Although this particular model is spendy ($50!) it’s still way cheaper and faster than taking shoes to the cobbler to be stretched. The only downside is that having this is enabling my “buy vintage roper boots on Etsy” habit something awful. There’s also a cheaper model that’s shoes-only, and another model that will stretch both length- and width-wise.
Sorry, people with narrow feet … there’s no corresponding shoe-shrinker. You’ll just have to be satisfied with being able to find vintage super-narrow Delman and Bally shoes everywhere you look …
[If you are all "ew, used shoes!" that's totally fine by me, leaves more for me to buy.]