It's the combination of the resistor in series with the capacitor and capacitor to ground that reduces the noise spikes. It acts like a filter.
The time constant, which is R x C, simply is a measure of the frequency response of the filter. This is typically defined at the point where the filter response is -3dB (0.7) of the DC response. This frequency in Hz is 1/(2*Pi*R*C). As the frequency gets higher the filter absorbs more of the noise with the attenuation increasing at 6dB per octave of frequency increase, since the capacitor impedance goes down with an increase in frequency.
I don't know if the above makes any sense to you but if you want to learn more I'm sure a Google search will turn up numerous articles on circuits and filters.