What do you think this black cable is for? What black cable is this? Black Romex?

Judging from the last two pics, it looks like 12/2 romex wire. 12/2 usually is a yellow outer jacket now, but it used to come in black. There is still white colored romex sold now too. So don't base your opinion on just the outer jacket color. There should have been a description printed on one side, flip it over and check. Another solution would be to get a "hot stick"(cheap) and check for live voltage just by laying the hot stick on top of the wire. If the hot stick goes off, you know you have at least 120 volts ping thru. Do you need it moved? If so, get an electrician. If not, just leave it alone.