555 IC - Transistor Tester
Capacitor connected to pins six and two is charged and discharged by the output pin 3. 

That is a common charge/discharge method for producing a 50% duty cycle.

Pin 5 can be left open like it is.  Normally a capacitor is connected from pin 5 to ground. Pin 5 is the control voltage reference for pins 2 and 6. So a bypass capacitor might be needed for better stable reference voltage.