A compressor attenuates the frequencies in the signal that exceeds the threshold signal level. The attenuation starts at the threshold, the amount of attenuation is determined by the ratio e.g. 4:1 means attenuate the signal by -4dB for every +1 dB the signal exceeds the threshold level. The attack time determines the time it takes for the attenuation to go from 0% to 100%. The knee determines the shape of the attenuation, whether it should be in a more soft or hard curvature and the release time determines the time it takes for the attenuation to go back from 100% to 0%. Make up gain is the amount of signal gain applied at the compressor's output stage, basically the amount of signal boost on the resulting signal. Peak or RMS are settings some compressors have to determine what the threshold signal level corresponds to, whether it is the RMS (average) signal level or the peak signal level. The modes can be mono, dual mono, stereo. For dual mono you can determine whether both the channels should be linked or unlinked, meaning whether each channel (L or R) should have their own unique compression or whether they should have a common compression applied on both channels. In Link mode the compression detector will calculate the maximum level of the two channels combined and compress both channels according to the maximum level using a single set of compressor configuration settings that are dedicated to the compression of the signal on both speakers. Essentially it means the threshold on each speaker is adjusted so that an equal amount of signal attenuation is applied on both channels (L + R), the amount of attenuation on both channels (L + R) corresponding to the greater amount of attenuation between the two channels (L +R). This makes the amount of attenuation equal on both sides but because the incoming signal level on each channel might be very different on each side, this can cause some stereo unbalance. Similarly, if you switch to unlinked mode you can also get an unbalanced stereo image, for instance one of the channels might become much louder than the other by the compression, causing a shift in the stereo weight towards one of the sides. That does not happen in linked mode as long as the signature frequency and peak/rms level on each channel is roughly the same. But if you do something funky, like move the bass guitar to one side and the vocals to the other, then you'll end up with issues with the linked mode. It is not true that linked mode narrows the stereo image, because the make up gain compensates for that. But compressors in linked mode impact on the stereo image because they can act more on the content in the center or more on the content on the side depending on the content of the signal. So in linked mode it's not generally a matter of getting stereo weight unbalance between L and R, it's a matter of width impact, but depends on the signal on each channel since the attenuation on each channel is equal and the perceived signal level is level relative (the dBu/volts RMS curvature is cumulative). Many compressors can be switched into mid side mode, this gives you greater control of the stereo width impact and at the process stage rather than at the input stage. Please be aware though that this compression is applied on an M/S encoded signal in isolation on each component then decoded back to L/R. It will hence separate the mid and side more, which may or may not be desired on the particular signal it is applied on. I guess one can say that when the L R weight moves towards one side, the unlinked mode becomes more interesting since it gives you greater control of the L R weight impact. Also be aware that a mix full of sound sources that fluctuate a lot in L R movement inside of the mix, can be distracting and can help lower the perceived separation of elements in the mix. But L R fluctuations can also be creatively used to excite the stereo image. How well it works depends on how it is done and on what.
The compressor is used to control the audio's timbre, whether that audio is a particular frequency band on a particular stereo channel (L or R) of a particular sound source or whether it is the whole mix, it all depends on what signal the compressor is applied on. The reason for this control is to shape the audio within the mix and to fit the audio within the mix. (in terms of fit - to utilize the full dynamic range of the playback format as efficiently as possible, both actual and perceived)