Normally in forums, social media sites, online chats, comment sections and so on, spammers, trolls, vandals (who usually try to disrupt the conversation with copious amounts of flooding), abusive people, etc. are quickly banned. Their account gets suspended or restricted so that they can't post anymore (either for a period of time, or permanently), or just outright removed.
Shadow-banning goes a step further than this. Rather than just inform the perpetrator that he can't post anymore because he has been banned, or even that his account doesn't exist anymore, the backend software hides this information from the perpetrator and makes it look to him like everything is normal. All of his posts appear to him as normal, as if he wasn't banned at all. They just don't appear for anybody else. Nobody else can see what he's posting.
One idea behind this is that this way the perpetrator will not notice that he has been banned, and thus will not try to bypass the ban (eg. by trying to create another account). For example this can fool a spam bot into thinking that it can still post to the site as normal, and thus it might avoid informing the bot software that its posts aren't going through (and thus, perhaps, avoid triggering a condition that will make it try to create another account, to keep spamming).
Likewise trolls and abusive people might not notice that nobody else is seeing what they are posting, and thus will be unaware of it, and will perhaps not try to circumvent the ban.
That sounds all well and good... in theory.
In practice it can lead to abuse. It would of course be nice if all forum/chat moderators were perfect, just and fair people, who always deal with problems in the fairest and most reasonable way, only resorting to bans when it's absolutely necessary and justified (such as to stop spambots, flooding, or people who are genuinely and excessively abusive towards others.)
But most people are not like that. There's a saying that "power corrupts", and it's very true. Experiment after experiment has shown that just regular everyday people, who are normally nice, polite and reasonable, tend to slowly become abusive when they get in a position of power, where they can control other people, and freely impose restrictions and punishments on them, especially if any such restrictions or punishment can be done with no repercussions whatsoever to deter abuse of power. It may happen quickly or slowly, but a good portion of people who would otherwise never behave like that in normal life, start slowly, even inadvertently, get "drunk with power" and start abusing it more and more, as time passes by, if none of their ever-increasingly abusive behavior has any repercussions. Of course, and definitely, not all people are like that, but many are.
So what happens if a discussion medium has a shadow-banning feature, and one of the moderators simply doesn't like some user, or dislikes his opinions, or heavily disagrees with him eg. on politics? Or what if a user writes criticism about the moderator in question, eg. about his behavior, and the moderator gets offended or pissed off about it? This can easily lead to abuse of power, where the moderator shadow-bans that user, just out of spite, or because of an ideological motivation.
Shadow-banning someone in this kind of situation can be quite devious, because that user may not notice it, and thus might not know to complain to the other moderators or administrators about the situation.
One has to also wonder how effective shadow-banning truly is for its "genuine" purpose. After all, an experienced troll, harasser or spammer can quickly check if his posts are going through by simply checking the site with another browser where he is not logged in with his usual account, and see if the posts from his actual account are becoming visible. If they aren't, it's quite clear what has happened. The effectiveness of shadow-banning may be much less than one might think at first.
When you think about it, shadow-banning seems more like a tool designed to be abused. It almost begs to be used to spite people that a moderator doesn't like, eg. for ideological or political reasons, rather than for any genuine purpose.
On the contrary, with trolls and abusive people it might even have the opposite effect from the intended. If such a person is just outright banned in the normal way, they might just leave it at that. They had their fun, or had their anger fit, got banned, and that's it. However, if they find out that they were shadow-banned instead, they might get pissed off and now genuinely try to circumvent the ban.
Ultimately, shadow-banning is a disingenuous technique, designed to fool people. It's not honest, open and up-front, instead using deviousness and dishonesty. It's not telling people "you committed a transgression against the rules of this site, therefore you are not allowed to post anymore"; instead, it's tricking them disingenuously.
I would say that shadow-banning has a lot more negatives than potential positives, and only leads to abuse and disingenuous behavior, giving too much power to people to abuse it for ideological reasons.