Low Voltage Disconnect and 2 negatives?
@SteveG pointed out that the 50 mA operating current at 12V suggests that the unit contains a relay. I agree. This is reinforced by the fact that the 24V version has a 25 mA operating current - ie double voltage but same power. This is typical of relays but would make less sense if it had a solid state switch. This means that the unit is probably but not certainly isolated between input and output when not operated. This would explain the use of two wires for each of input and output. You can check for non operated isolation as mentioned below. 



Their spec sheet  is 
inadequate.   

If the unit contains a relay it is probably input-output isolated when not operated. (A relay will make a nice comforting click when operated and you can perhaps feel it operate as well if you hold the unit.)

If it uses a 'solid state' switch then it is PROBABLE but not certain that the 2 negatives are hard-joined electrically, and that the extra wire is for convenient connection.
An Ohmmeter should confirm this, or not.
Also, when isolated, check connections and voltages on output leads. 

While it is possible to make such a device with semiconductor switches and also with true floating input/output when in isolate mode this would be unusual.
ie usually you get a SPST switch with common grounds
rather than a DPDT switch.