What is the purpose of a low-pass filter used at the output of a digital-to-analog converter?
Why A DAC builds its output from discrete steps at the sample rate, so the waveform is really the desired signal plus copies (images) of it centered on multiples of the sampling frequency, along with the sharp-edged staircase harmonics. A low-pass reconstruction filter set just below the Nyquist frequency (half the sample rate) passes the wanted audio or baseband signal and strips off those higher-frequency sampling artifacts, smoothing the steps into a clean analog waveform.
Watch out The idea about lowering input bandwidth to increase resolution describes anti-alias filtering ahead of an analog-to-digital converter, and resolution is set by the number of bits, not by filtering; nothing in an analog output filter can sort out out-of-sequence digital codes.
DAC out = reconstruction filter: smooth the staircase, kill the images above Nyquist.