I know why we need a pull-up resistor on the reset lines, but what is the reason for a capacitor parallel to the reset button?
I saw it on Texas Instrument's schematic for MSP430F5529 launchpad.
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It is for "debouncing" of the pushbutton. Virtually all pushbuttons, when pressed, do not make a single clean contact, but instead make several repeated contacts within a period of 10-50 ms. This would cause the microcontroller to begin to reset several times on each pushbutton press. The capacitor suppresses this.
For more information on debouncing, see this article.
The capacitor provides certain reset time, which is normally required to ensure all registers are cleared. This implementation is not very clean, because on power off the capacitor will remain charged, applying voltage on reset pin. Which nowadays is not a problem, the clamping diode will discharge it. But once it could damage the input.