(1) To make a digital audio signal smaller by lowering its sampling rate or sample size (bits per sample).   Downsampling is done to decrease the bit rate when transmitting over a limited bandwidth or to convert to a more limited audio format.  Contrast with 
upsample.  See 
sampling.
(2) To decrease the color depth of a digital image; for example, from 24 bits to 16 bits per pixel.  Contrast with 
upsample.  See 
color depth and 
downconvert.