Saturation refers to the introduction of a harmonically pleasing overtone series. Unlike distortion which provides a spectrum-wide agitation of harmonic content, saturation provides harmonics that are relative to the input signal. This method of introducing harmonics was discovered when engineers would over-drive an electrical amp device such as a microphone pre-amplifier. Over-driving the electrical circuitry by a nominal level would introduce an extremely pleasant colour to the sound being recorded and that effect became known as saturation.
When over-driving a device, it causes the sound to become clipped as the output indicated by the setting exceeds the performance of the circuitry, thus means must be made to prevent the sound from exceeding the physical capacity of a device. This means of governing a signal can be created with further onboard circuitry or even strength of the mechanism itself. Think about over-driving a bad speaker, beyond a certain point you begin to notice distortion and crispiness that gets applied to a sound. This distortion is created by the very pushing of the limits of the capacity of the device or onboard safety circuits that provide limiting functions.
The nature of analog sound being electrical provided a very warm type of distortion known as saturation while digital devices provide a very cold method of distortion. In any case, saturation and distortion is ultimately the limiting of a sound by increasing the input to hit a particular governing device such as soft clipping diodes, hard clipping digital ceilings or PWM encoding on export.
Too much harmonic distortion is detrimental to the low end of a sound, if you notice power starting to dwindle, back off on the drive parameter on the saturator or revert back to the post-EQ to balance out any inconsistencies.