relays have 3 possible power supply connections.
the Output is isolated from the coil and logic, and really the only possible connections are the leaks in the PCB. the relay PCB has a physical cut out of the PCB around the Common pin, in an effort to prevent these sort of leaks.
the second power supply, the coil voltage, is determined by the coil manufacturer and you must supply a voltage that will supply power to the coils.
Since this board has opto-isolators, you have the possibility for that 3rd power supply.
the jumper for VCC and JD-Vcc will connect your coil power supply to the opto's thereby tying the two power supplies together and removing one layer of isolation. but, then all you need to do is to bring that line to ground and then the coil operates.
as you can see in the manual for the board, or the post that Terry King posted, the opto can also be powered strictly and only with the Arduino on Vcc. if used that way, the opt-isolators appear to be simple LED's to the Arduino. a resistor is needed like any LED you might drive.
using the opto-isolators independently of the JD-Vcc gives you better isolation, and tying the grounds together defeats that.