Relay does not trigger
NC is "Normally Connected" - this contact is connected to COM ("common") if coil of the relay is not powered - the relay is disconnected.

NO "Normally Open" is connected to COM when the coil of the relay is powered - the relay is connected.

Some relays have the coil powered when the signal from MCU is LOW.

If the coil of the relay doesn't click, but the signaling LED lights up, then VCC is not connected. Check if you plugged the wire really to 5 V on Arduino side.