Motion sensor circuit question
That arrangement is known as a Darlington pair. It gives a current gain of the product of the gains of the individual transistors.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A more common Darlington arrangement.

A small current injected into the base of Q1 will cause a large emitter current which will flow into the base of Q2 causing an even larger collector-emitter current in it.

Theoretically, if Q1 has a current gain of 50 and Q2 is the same type then the combined pair have a current gain of \$ 50^2 = 2500 \$. This allows tiny signal currents to switch large loads.

In your schematic the small signal is provided by the PIR sensor. The relay forms the "large" load.