When you're mastering for vinyl, understanding mid/side processing is essential. The way a cutting stylus translates stereo information into groove modulation is fundamentally different from stereo recording, and if you don't account for this, you could run into problems ranging from distortion to unplayable records.
Mid/side processing splits your stereo signal into two components. Mid is everything identical in both channels, centre panned content like vocals, kick, snare, and bass. Side is everything different between left and right, your stereo width like reverbs, delays, and panned instruments. A cutting stylus doesn't cut left and right channels independently. It cuts in two axes: lateral modulation, where the stylus moves side to side in the groove, represents your mid information, and vertical modulation, where it moves up and down, represents your side information. So mid equals lateral movement, side equals vertical movement.
This matters massively for things like bass. Low frequencies carry huge amounts of energy, and if you've got bass that's panned or out of phase between channels, you're making the stylus to do large vertical excursions. Vertical modulation is inherently harder to cut and play back than lateral. In the worst case, if severely out of phase, the vertical modulation makes the cutting stylus literally lift out of the groove, meaning an unplayable disc.
If you're using a feedforward system where you're correcting for cutterhead frequency response in software, M/S becomes even more important to understand. You're already applying significant EQ for mechanical resonances, so feeding it a signal with phase problems worsens the issue. You should apply M/S processing in mastering before the signal hits your feedforward EQ.
A good beginner's tip is to use dynamic EQ software, such as Tokyo Dawn Labs' Nova GE. First, we should note that mid/side is also known as sum/diff, which is the terminology this plugin uses. You can set Nova to affect purely the diff signal and use it as a dynamic EQ with up to six bands. Their 6 Band Dyn EQ preset is a great place to start. You can set the threshold and ratio of each band independently, and the meter will give you a visual reference of the audio too. Keep an eye on areas that get spikes or lots of energy, particularly in the low end, the midrange around 2kHz, and the upper mids around 7-8kHz. These are problematic areas on disc, especially in the side/diff signal.
Don't go too heavy handed, you want the side signal controlled, but not killed. The main thing is to catch buildups of energy and make sure the EQ reacts efficiently to pull back parts that peak. You can also solo each band to check what's going on in that area. This isn't a one size fits all kind of thing, and learning audio mastering is always essential, but it's a good starting place if you haven't looked into mid/side sum/diff processing before.