Light days can accomplish a variety of different things depending upon the situation and the lifter's level of training advancement. To address your most basic question, an Advanced Novice is capable of two weekly squat increases, let's say Monday and Friday. His stress->recovery->adaptation cycle is still pretty short and simple to manage but it's now 3-4 days instead of 1-2 days. So a light day in that program allows for technique practice of the lift, as an Advanced Novice hasn't been doing the movement for that long yet that technique is perfectly ingrained. It is a perfect day to work on the technique issues that may pop up on the heavier days but are difficult to address because of the weight on the bar. Obviously technique issues beyond a certain level of degradation call for taking weight off the bar altogether, but smaller errors and issues that don't approach unacceptability but are still not ideal, are hard to work on at heavy weights at which your "auto-pilot" kicks in and you resort to your pre-programmed motor pattern to get back up out of.
At the same time, this day must not be so heavy that it is, in and of itself, a new stimulus/stress to be recovered from, because it will take the 3-4 days to recover from the previous heavy squat session and be ready to add weight to the next. But it also can't be so light that the weight isn't even felt, or the weight of the lifter/barbell system is SO different in a work-set compared to light day that the feeling of keeping that system weight over mid-foot isn't even simulated on the light day. Then no technique practice has been accomplished. (The getting increased blood flow to the area will probably still help with recovery even at lighter weights, however.)
All that said, 80% is not set in stone. I always tell lifters to err on the lighter side, but it'll probably end up being around 70-80%. 60% of the working weight isn't "wrong," per se, but is probably too light for almost all Advanced Novices to provide meaningful technique practice. When would 60% of Monday's workload be more appropriate on Wednesday? Only if the fatigue from Monday's workout is deep, and the soreness intense. Otherwise, Advanced Novices should probably be handling at least 70% on light day, closer to 80% if it's not too much.
At periods later in someone's training career, this of course will be very different. This is specifically about the Advanced Novice stage.
In many ways (though not perfectly so), a press is automatically "light day" for bench. This is less the case when you're pushing press to the end of its limits on LP, but for the majority of the program it serves that way.
And PC and later PS, are "light days" for deadlifts. The longer ROM of the olympic variants does increase the total work done but they're so much lighter that they still provide recovery for the muscles involved. I've never coached a single lifter who had an issue with their heavy DL anywhere in the Novice program because of the cleans and/or snatches they did. Whereas almost every lifter's PC and/or PS are limited at the end of their LP because of residual fatigue carried from their heavy squats and DLs.