The bistable configuration is stable in both states, staying where you put it.
In this configuration the 555 is being used as an RS flipflop. It simply exposes the operation of the internal flipflop.
Making the trigger low briefly sets the flipflop, making the output high. When reset is made low briefly, the flipflop is reset, making the output low. In this configuration, discharge is not used and left unconnected. Similarly threshold is not used, but it needs to be connected to ground to make sure it stays well below 2/3 Vcc.
While this may seem like overkill, it does give you an RS flipflop in a small, 8 pin package with a very flexible supply voltage. Alternatives would be using a 14 pin chip or building a flipflop from gates or transistors, both of which would take considerably more space and likely have supply voltage restrictions.