Gamut Mapping
The process of converting colours from a larger space into a smaller one while preserving as much of the image's appearance as possible.
In depth
Mapping must decide between accuracy and relationships: clipping out-of-range colours to the boundary keeps everything else exact but destroys gradation, while compressing the whole gamut preserves separation at the cost of shifting colours that were reproducible all along. The rendering intent chooses between these strategies.
Examples in practice
A deep blue sky compressed rather than clipped keeps its gradation from horizon to zenith when printed.