When the output of the PIR's pin 2 is 0v, the base of Q1 is low, turning OFF Q1. Q1 appears as an open switch, so you will see +12 on both ends of the relay coil. When the output fn the PIR's pin 2 is +3.3V, the base of Q1 is driven to +0.6V through R1, and Q1 is turned ON, like a closed switch. The lower end of the relay's coil is then pulled to ground by Q1's collector, turning on the relay.
In you relay pin-out connections (lower left), you don't need to connect the coil pins to the NO and NC pins.
Ken