The circuit is a motion detection alarm circuit, I know what the circuit does but I want to know about the resistors attached (R2 is attached to the transistor for amplifying the output to 5V). Why R1 and R2 are attached? Anything do with the delay? Can you explain to me the relay circuit of npn transistors?
R1 protects led 1 from dying.
R2 protects q1 from dying. It also sets the base current that is multiplied by the gain of the transistor to allow that much current through the C-E junction.
Diodes like led 1 and the base of a transistor must be current limited so they don't go into a overload condition and burn out.
The delay is completely internal to the PIR module.