The 555 operate at 2Hz. Output pin 3 drives the circuit with a positive then zero voltage. The other end of the circuit is connected to a voltage divider with the mid-point at approx 4.5v. This allows the red and green LED's to alternately flash when no transistor is connected to the tester.
If a good transistor is connected, it will produce a short across the LED pair when the voltage is in one direction and only on LED will flash. If the transistor is open, both LED-s will flash and if the transistor is shorted, neither LED will flash.