A side chain is essentially a copy of the input signal used to modulate (or control) how a device operates. If a device does not have a side chain send/return option, that means it will either use a copy of the signal itself or that it will do some internal processing (to a copy of the input) in order to achieve whatever sound it's trying to achieve. It's important to note that it's always a copy of the signal, and not the input itself. This means that whatever happens to the side chain signal, it does not apply to the audio being processed.
The most common use of side chain processing is with compressors. Due to how much energy low frequency sources have (like the bass drum on electronic music or a bass guitar in rock), these sources can very easily trigger a compressor even though the rest of the material in the input signal doesn't require compression. On those situations, adding a high pass filter to the side chain signal makes it so the compressor will be less sensitive (or completely ignore, depending on the filter) to low frequencies.