I Believe That a Man Can Shoot FireballsImmersion is the ability to lose oneself in the fictional world of the medium you're consuming, to be really broad. It's the big thing you want to achieve as a game developer.
Immersion is, however, not based on making it look real. If it was, all games could just throw it out of the window, since you will always have something that's not 100% realistic, especially in terms of graphics. See my post on realism.
Immersion vs InformationI once read a blog post which kind of pissed me off. It was largely a rant on how menus, stats and figures destroyed the immersion. The example was the SNES classic Lufia, and the argument was that the numbers are not part of the world.
Eeeh, I say. Sure, the numbers and interfaces aren't part of the world, but they're part of the gameplay. They tell you how well you do, how much you get stronger and if it's really worth to buy that new shiny piece of armor. Increasing stats and levels show you that you have, indeed, gotten stronger. This is part of the game. And if your immersion is ruined by stats, then, maybe, RPGs are just not your kind of game.
Sure, there is such a thing as too much information. No one wants to fight themselves through tons and tons of stats that may or may not do something.
Perfect ImmersionI realized something: The games with the best immersion possible are the ones where you play a dude in front of a computer. Because then, you are the dude in front of the computer.
As I said, I played Digital last night. It's a game where you are, surprise, a dude in front of a (really old) computer. In the end, I was equally drenched in feels and geeking out over the references. Have I mentioned that you play a dude in front of a really old computer? With dial-up internet (modem sounds are oddly calming to me) and old school BBS. At one part, you could download a patch for your computer's OS that fixed a buffer overflow bug. It actually required you to restart.
Outside of the configuration screen, this game has not broken immersion. And you know why? Because text and stats and menus are the game, so they can't break it.
But not all games are "dude in front of a computer" games. So not all games can go all the way without losing information.
The FilterThe Filter is what makes immersion possible. I'm pretty sure you noticed it before, so I'm going to explain. When you play a game, as you get into it, you kind of see it through a filter. You become immersed in it. I'm speaking for myself here, but I tend to dismiss the UI on the screen when I look at the world. In the context of the game, it's not there, and after a while, you'll be ignoring it. Sure, it's there, and you still look at it for your stats, but somehow, you don't mind. Your brain can do that. It's awesome that way. And this is why an on-screen UI doesn't matter, unless it's so damn huge that it's impossible to ignore.
In-Game DisplaysAgain, this is subjective, but I have more problems with shoehorned in-game display of stats than with stats in a menu. Because as soon as something's outside the UI, it's part of the game's world. You need an explanation for how it works. You can't just say "HP are a thing now, deal with it" and go on with your business.
The problem with in-game information vs UI information: Many stats and other things are abstractions. Health can't be measured in points. How do you explain ability points? Or levels. All these things are somehow abstracted and meant to be representations and shorthands. Just like toilets are abstracted out of games. And as soon as you put them back into the actual world, you have to think about the logic behind them.
Long story short: I'd rather have a UI that has been thought through than a shoehorned-in in-game thing. Mostly because the latter kills my immersion much more, since it pulls game elements into the world.
Screw Immersion, I'm a Video Game CharacterThe other way to approach it is to screw immersion and go meta. You know it's a game. And so does everyone else. Expect characters finding out each others' names because they're in the text box, calling you out on your sucky play style and fading to black so that you don't watch them undress, because that would be creepy.
Warning: Meta writing is difficult. Only try it when you're absolutely sure you can do it, as it can quickly be extremely annoying. Also, meta doesn't necessarily mean "cheap fourth wall shattering jokes."