I think that hose on the outside left is for filling the barrel... and/or making a siphon that empties the barrel.

Oh, I know this one.

The elevated barrel usually indicates that water pressure is only sometimes available.

For example, the available pump might be solar powered and batteryless, or just a manual hand pump.

In either case, the water being elevated allows people to use the shower even when the pump cannot operate - at night, if solar, or just some people don't have the physical fitness to operate some hand pumps.

Edit: All of that to agree - this setup is typically awkward as fuck.

Edit 2: Also, the barrel can also serve to warm the water from frigid underground running water temperatures up to "water that has been sitting in the sunlight" temperatures.