This is one of those many cases where it is hard to tell what the installer was thinking. "Car stereos", as we call them, have two positive wires. One power wire will typically come from your main DC fuse or breaker panel and will lose power when the main battery switch on the boat is turned off. The second wire can be connected to the same place, but ideally it will go to the battery before the main battery switch. This allows your clock and saved radio station memory to stay intact when the main switch is turned off. Both of these wires need to be fused at the power source, whether it's the battery or main DC panel.
In the picture someone has wired the main power wire (red) correctly to the fuse panel with a fuse. But the yellow battery cable was wired to the incoming power of the fuse panel. Our best guess is the installer was confused on the difference between fused vs. switched and that by connecting on the main line before the fuses, they considered it the same as "battery". The yellow cable is now un-fused, but is still switched off by the battery switch. By attempting to do something they thought was correct, they ended up doing two things wrong. The simple solution was to put the yellow wire on one of the empty fuse terminals which is where it was moved to. No saved radio stations, but also no fire hazards from having easily fixable un-fused wires.