When an image is prepared for printing, it is converted from its color space (whatever that may be, often RGB) into the color space of the printing device. When that occurs, a separate image is created for each color ink on the printing device. These are the Separations.
For instance, in printing to a CMYK printer your image is split into separate Cyan, Magenta, Yellow, and Black images. Each image corresponds to the amount of ink of each color that the printer requires to reproduce the image in "full" color. (simulate full color by combining the separations).
There can be an almost infinite number of CMYK combinations that will reproduce the image and each group of separations is unique to the specific output device. This makes color separation as much an art as it is a science.