The function of a fuse is usually to prevent fire - that's the basic protection a fuse offers - between power supply and appliance there may be a few feet or metres of cable - if a short circuit occurs in the appliance, the cable could easily become overheated (due to excess current) and burn or rupture its insulation. Without a fuse to "protect" the cable, this can lead to the direct ignition of material in the home or workplace and suddenly what starts off as a minor incident ends up with a building burning to the ground.
Side effects of course are danger to anyone coming into contact with ruptured cable and receiving an electric shock. A fuse prevents this by protecting the cable.
When it comes to protecting "loads", a zener diode and fuse perform a slightly different job. They are called zener barriers in the petrochem and coal industries because they limit the voltage at the terminals of "otherwise safe" equipment and this significantly reduces the risk of an ignitable gas explosion or dust explosion.
In your case F2 just protects the equipment that is connected to your output and F1 likely protects the cable between power supply and appliance.
See this wiki article