Brass Pipe Fitting, 1-1/4 x 1 Inch Hex Bushing

Exactly. This hex bushing steps down from a 1-1/4 inch pipe size to a 1-inch pipe size.

Right on both counts. The male end is 1-1/4 inch pipe thread and the female end is 1 inch pipe thread, so it reduces from the larger pipe side down to the smaller one. That's the whole job of a hex bushing, and this one handles that transition in standard pipe thread sizing. The hex body gives you a good flat surface to grip with a wrench when you're threading it in.