This object is colloquially called a Dutch* Broom Hanger.

It's a low-tech way to hold cylindrical objects to the wall.

As for how it works, ignore the Romanesque shape of the ones above, that's a stylistic element that has nothing to do with the object's function. Inside it looks like this:

When you push a broom handle up from the bottom, the roller (which can just be a length of dowel) moves up the incline. As you release the broom, gravity brings the roller back down, and friction causes it to pin the broom handle in place. To release the broom, you simply lift it upward and toward you.

If you didn't want to capture the roller both front and back—if, for instance, you wanted to see the mechanism—you could do this by capturing the roller at the back, using a protrusion on the roller and a track in the rear panel.

The object also lends itself to 3D printing.

StageTop on Etsy

StageTop on Etsy

StageTop on Etsy

StageTop on Etsy

Printable Accessories

Printable Accessories

Printable Accessories

Printable Accessories

*It's called a "Dutch" Broom Hanger after the Pennsylvania Dutch, who are of course not Dutch at all. ("Dutch" is a bastardization of "Deutsch;" the Amish originally migrated from Germany.) The Amish popularized this design sometime in the 18th or 19th century, and still sell them today.

A more modern version of this design eschews the internal ramp and uses a cam instead.