I constantly hear people say to use /camp when you encounter a bug, but I have never had this work... so im curious what exactly are people talking about?
The title of your post is called "How does /camp work in regards to changing instances?" Doesn't say anything about bugs in the title, but then you ask about bugs in the post, and never mention changing instances. I believe that's what @RSram was referring to.
In answer to your question, I've never used seen anyone recommending using /camp in game, so not sure what it does, if anything.
/camp supposedly allows you to log out and then log back into a different instance. Changing your instance is thought to be a potential bug fix.
However, based on my personal experience with using /camp and from what I gathered through some quick googling, /camp just seems to be another way to log out, without any impact on which instance you are placed in.
Relogging simply gives you the chance to reset a bugged event. I had some cases where NPCs wouldn't spawn or get stuck and a quick /camp helped there. /bug is there to simply report your problem, /camp if you want to try to get around it without waiting for a GM to fix it for you.
/reloadui also has a chance to change instances, but for any of them to work there must be other instances to join.
/reloadui, /camp or ALT-F4 where used a lot during the beta testing to get around quests/spawns being bugged but I'm not sure that they do as well now.
But if you come across a quest not updating or a spawn not appearing they are worth trying, with a 20min logout or avoid that area as the last resort.
“Be as a tower, that, firmly set,
Shakes not its top for any blast that blows!” Dante Alighieri, The Divine Comedy