The double-pole switch selects between testing a PNP or NPN. A 9V battery connects between +9V and the ground symbol. No on-off switch required if no transistor is left plugged in the socket. A shorted or leaky transistor would kill the battery even if the Test switch is open.
A good transistor lights a LED only if it has some current gain while the Test switch is pushed. Which LED lights is determined if an NPN or PNP transistor is being tested.
If the transistor is open, neither LED lights. If an LED is always lit, then the transistor is shorted. A refinement would be to use a Red/Green inverse-connected double LED (in one package) for the two shown in the schematic.