iotcom:
maybe because it needs external power supply (arduino and the relays)
Could someone help me with if that's the problem and also what power specs should it be (Volts and amps).
Yes the certainly need an external power supply.
The document in your link provides the specs - 5v, 12v or 24v with a minimum current of 750mA for each bank of 8 relays. It says the use of 24v causes the board to get hot so I suggest using 5v or 12v. A USB charger that can provide 2 amps should be suitable.
SONGLE relay draws 72mA, not sure about the load for the rest of the circuit.
since you said you are powering from 5v, we know which board you have.
With 16 relays and say, 80mA you would need about 1,200 mA.
Robin2 said that the board you linked has 750ma for 8 relays, so they may have added some load for relays and such.
Robin2 was spot-on with a 2 amp power supply.
The link did not show that the signal ground and the relay board ground must be tied together, but to complete the circuit, they will need to be.
Just to add to Paul__B's post. The Mega's recommended range is 7 to 12 volts FROM THE BARREL JACK. That is fed through an onboard regulator to supply the board with 5v. If you don't have a supply in the range from 7-12. You can connect a regulated 5v (phone charger) to the VCC pin of the board.
The point here is that you can power the Mega with 7 to 12 V via the "barrel jack" - or "Vin" - but only the Mega itself.
In this situation, he wants to power a set of relays which operate on 5 V so he needs a 5 V supply to operate them. It makes no sense to have a 5 V supply for the relays, and then provide a separate 7 to 12 V supply just to operate the Mega board! Once you have the proper 5 V regulated supply, you use it to power the Mega as well.