Curves can usually be applied to all channels together in an image, or to each channel individually.
Applying a curve to all channels typically changes the brightness in part of the spectrum. The software user may for example make light parts of a picture lighter and dark parts darker to increase contrast.
Applying a curve to individual channels can be used to stress a colour. This is particularly efficient in the Lab colour space due to the separation of luminance and chromaticity, but it can also be used in RGB, CMYK or whatever other colour models the software supports.