I built a project with the help of a breadboard diagram. Now I want to understand what this circuit does. How does this circuit work? I am looking for an analysis of this circuit diagram.
IC1 is an astable multivibrator, producing a 26.6 Hz square wave on its pin 3, with approximately 60% duty cycle. It's a classic 555 circuit, and you can read more about how this works and the frequency calculation at Wikipedia page about the 555 timer chip
That will flash the LED L1, but probably too fast to see.
When S1 is pressed, this signal is applied to the clock input of the counter IC2. This is a CD4017 decade counter. This counts input pulses and makes one of its outputs high, thus lighting one of the LEDs on the right, L2 to L11. When it gets to 9, it goes back to 0.
It will behave somewhat as an electronic random number generator, choosing to light one of the LEDs depending on how long you press the switch for.
Just for completeness: R1, R2, C1 control the frequency and the duty cycle; C2, C3 decoupling; R3, R5 LED current limiting; R4 pull-down; Diagram wrongly says 4017 is a "BCD counter", but actually it's a decade counter.