It boils down to: if variance didn't exist, this is roughly the number of goals expected from the chances a side has created.
If you want a discourse on logistic regression, why that's the appropriate methodology, why maximum likelihood estimation is usually the method used to fit the curve and how switching up model parameters and methods of fit will cause discrepancies between various sources for xG, I can try to explain the basics...but you'll probably tell me to stuff it inside of five minutes, so I'll give that a pass.
The layman's explanation is pretty straightforward: the type of model being fit is much the same sort of thing medical professionals do when they're trying to figure out how much this risk factor or that risk factor affects things like mortality and morbidity rates, just without the time component they're dealing with. We're trying to predict a result with two states - goal or no goal, which is much like the medical professional trying to explain dead/alive or disease/disease-free.
The approach has problems. In principle, we should have horked up as many goals as Leicester (18-19) per xG. We have admittedly gotten lucky in a couple of games, but the model is positional in character and can't deal with things like good finishing, good goalkeeping and good blocks. Trying to do that results in trying to attribute more impact to players than we have enough information mathematically to justify, so the model has to sweep those attributes up in the variance term instead. You'll see more sophisticated models take defensive positioning into account, because that's doable, but player identity just isn't going to work because there's too many attacker/defender/goalkeeper combinations relative to the number of shots taken.
With a long enough data series, it starts becoming apparent that Messi was a very good finisher until he went to PSG. The model can't tell you why, though. It could be that the through balls he was getting were absolutely disgusting, it could be that he did dirty things to defenders off the dribble until recently, or it could be some combination of those or other factors. All it can say is that he was an outlier.
My advice would therefore to be to take any prediction of regression to the mean with a grain of salt, if you have cause to believe otherwise. xG will tell you that Haaland shouldn't be scoring as much as he is, but that's nonsense. He's just lethal, and he's proven that in previous seasons. It will tell you that we should have scored more goals than we did last season, but things like garbage long balls taken by a low-percentage shot-taker will fluff up xG without actual expected results. The model implicitly assumes that Gray is as likely to bomb in a worldie from distance as Cristiano Ronaldo, which we know isn't true.
TL;DR: xG is a good tool if you understand what it does well, and what it doesn't. Most people don't, and misuse it as a result.
