How to read a schematic with capacitors
There is no one set answer; capacitors can perform several different functions in circuits.  In all cases there is charging and discharging going on, but how that affects circuit operation depends on the circuit.
Both of the schematics you posted have capacitors performing an R-C timer function.  A capacitor is charged up or down through a resistor until the voltage across the capacitor passes a certain value, often called the circuit's trip point.  When that happens, the circuit does something.  Exactly what is different in the two circuits, so pick one and we can drill down into its function.