[obiwan53]

It is indeed used to carry the saber higher while dismounted. Simply hang your sheathed saber from the sword hook by the scabbard's top ring. You see, normally a cavalryman's scabbard straps would be set to a length which works fine while mounted but the scabbard chape could drag on the ground when dismounted. If you are tall it doesn't usually drag, but it's still going to hang at an obtrusive angle. It's rude to bump people with your scabbard. The sword hook resolves that problem easily, although the scabbard will still bang against your leg if you start moving around much. When hung from the hook it hangs pretty close to vertical and is far less likely to cause offense. People that never wear the saber on horseback often simply shorten the top strap enough so the scabbard chape doesn't drag and the weapon hangs politely without using the hook -- but then they're not wearing the cavalry saber in true cavalry fashion.

Years ago I used to be a Civil War cavalry reenactor, so I speak from some experience.