Yes, that is the regulator. What it does is convert the A/C current produced by your stator and convert it to D/C with about a 14.5v output to charge the battery and run some of the lights and accessories. (usually brake light, turn signals, horn, fuel gauge) On some models it also runs the cdi. If your engine runs without the battery or regulator, then you have an A/C cdi which runs directly off of the stator.
What happened is your regulator probably went bad and was putting more than 14.5v to you battery. When you jumped the fuse, the excess current fried the wiring.