During bit-depth reduction, e.g. from 24 to 16 bits, quantization errors can introduce unwanted distortion. The process of dither can counteract that distortion. A low-level noise source is introduced, and the noise (called dither, typically white noise that has had filtering applied, often called noise-shaping) prevents the squaring-off of waveforms around the least significant bit, thus keeping the signal just above the threshold of the least significant bit. This results in smoother sound at the reduced resolution (lower bit rate).
Dithering is programmed into devices and software programs, and different programmers do it differently, so choosing one device or program over another to do your bit-depth reduction can produce greatly differing results - trial and error is often recommended.