IF the relay uses 5VDC for activation, THEN if you connect terminal 4 to DC ground, the relay will be turned on whenever the 5VDC power supply is turned on. On the other hand, if you want to control the relay some other way, then you would connect terminal #4 to a circuit that is ACTIVE LOW (perhaps a signal line from the break-out-board?).
It looks to me like you have a classic Solid State Relay circuit that could be operated by a TTL LOW signal. In the process control computers that I have designed, I would often connect an I/O line from a microcontrol processor directly to the (-) side of the SSR's control inputs. Then, the control program for the microcontroller could turn the SSR on or off.