Take a look at the visual explanations. All parts connected to the negative terminal of the battery (0 Volt) are shown in blue, all the components on a positive voltage (>0 Volt) are shown in red.
After connecting the battery, the LED2 lights up...
You press S1. As a result a positive voltage applies to the basis of the transistors T1...
Now, the push-button switch S1 is open again and the capacitor C1 is charged through the resistor R1.
Once the capacitor is charged, the voltage at the base of transistor T2 starts to rise.
Once the voltage at the base exceeds 0.7 Volt, the transistors T2 switches through and the multivibrator returns to the state from first step.
What influence has now the capacity of the capacitor...?