When power is applied, the current goes via the capacitor and the voltage of capacitor increases slowly. At the beginning, the voltage is lower than the reset input pin threshold voltage and all elements in the CPU are hold in reset mode.
The capacitor has no charge on it, so the voltage across it is zero. As the capacitor charges, the voltage across it increases, the voltage across the resistor decreases, and the voltage on the Reset pin drops towards Ground. If that's the wrong way round for what you want, swap the capacitor and resistor over.
For a controlled signal on the line. Many MCUs have reset timing that must be enforced and the capacitor is a cheap alternative to e.g. a supervisor IC. The capacitor provides certain reset time, which is normally required to ensure all registers are cleared.
Those are almost always due to poor circuit design and inadequate power supply decoupling, leading to large dips in the voltage. A large capacitor on the reset pin is not the solution. Yes it will stop the Arduino resetting, if that is what you want. But it will also stop you loading code into it. It is best to put a switch in.
Assuming the inversion that happened in your explanation versus the picture is taken care of, and when capacitor is charged, there will be GND at reset pin, if no current flows out of reset pin. The way that is drawn, when the system is first powered up, the Reset pin will be pulled up to VCC.
When the RST pin has a high level for enough time to reset, and then returns to the low level to enter the normal working state, the typical values of this resistor and capacitor are 10K and 10uF. (2) Button reset: Button reset is to connect a switch in parallel on the reset capacitor.