Spectral noise transformation in a quantisation processes. Noise is "colourised" in the time domain an/or frequency domain by adding parts of the previous sample. The SNR bandwidth and SNR time integral stay the same, so some noise decreases, some increases, but overall noise always increases.
An example of noise shaping in the frequency domain is quantisation of samples on a Compact Disc to reduce noise below -98 dB. The are different algorithms with slightly different filters, e.g. Super Bitmapping, 4D Recording.
A time domain example is MPEG-4 AAC TNS, which is a method to enhance quality by temporal forming of the noise in a transform block.