Gaussian filter as a low pass filter
it's because all of the filter coefficients (which is the impulse response $h[n]$) are positive and there is no "ringing" in the impulse response.

so, assuming the impulse response is scaled so that all of the $h[n]$ add to 1, the output of the gaussian filter will be a weighted average of the input.  averaging is a process that removes high-frequency variation.  so what is left are the low frequencies, like DC.  that's what a low-pass filter does.