The circuit is basically a 555 astable circuit that divides two LEDs, LEDl and LED2. LED2 is switched on when the output of Ul is high, and LEDl is activated when its output is low. When Ul oscillates, LEDl and LED2 switch on alternately as the output of Ul switches from state to state. Resistor Rl`s value is high in comparison to R2, so the waveform at the output is a square wave with a mark/space ratio of nearly one-to-one.
When you release Sl, you break the circuit and Ul latches whatever the output state happens to be at the time.