It's hard to say from the out-of-focus photo, but I'd give equal likelihood to overheating (due to arcing or motor failure) and physical damage. That scuff looks vaguely like what you'd see if a drawer or something pinched the cable or repeatedly rubbed against it.

The bottom line is that it needs to be replaced as the copper conductor looks nicked. Whether the disposal motor is on its way out is anyone's guess.

That does look like heat damage. It's possible that if the disposal jammed and the cord was pressed against something that the current draw heated the wiring enough to melt the housing like that.

UNPLUG THE DISPOSAL AND DON'T USE IT UNTIL THE CORD HAS BEEN REPLACED

Under your sink, in a wet location, having exposed wires is very dangerous. Your disposal may have a replaceable cord-set, which means that you can unscrew this old one from the disposal and install a new one by screwing it in, or, if it doesn't you might get away with cutting off the damaged piece and installing a replacement plug. Worst case, you may have to replace the whole disposal.

You can do some testing on the disposal. With the breaker off, see if you can rotate the inside plate, use a broom handle or similar item. There is also a reset button on the outside bottom of the disposal, make sure it's pressed in. There should also be a hole in the middle of the outside bottom where you can fit an allen wench, I think a 1/4", to turn and free the plate if it's stuck. Try running the disposal to see if it works. If it does, turn it off and replace the cord. The cord looks like it came in hard contact with something like @isherwood said. It could have been done on a previous disposal replacement. The copper conductor is damaged and needs to be replaced. People reach under their sinks way too often without looking to have something this dangerous lurking around. If the disposal doesn't work, then a replacement will be needed.