I can't just write a definition, however, IMO there are a couple of things which increases the immersion.
- Mechanics and lore being in line and making sense in the context
- First person perspective
- Music fitting the ambiance.
- More realistic or gothic artstyle.
- High lethality(except in few ocasions where low lethality makes sense)
- Reactivity
Mechanics definitely. Things not being logical (or logical in terms of the virtual world as set up) are really jarring.
FPP no, not necessarily. This is a hobby horse of mine. FPP is "more immersive" only in a specifically dungeon-crawling context, where it mimics the tunnel vision you get from fear. In most other contexts, TPP is more immersive because it mimics the sense of oneself that one normally has of a 3-d entity situated in a 3-d world, which you get from subtle environmental sensory cues, from the eyes' constant saccading, etc., and from the brain's own modelling of its body situated in the world. The only downside of TPP is being able to look around corners, but that can be solved by adroit use of fog of war. Being able to switch between the two is best (e.g. in the Bethesda games, you can be in FPP when you're inching through a deep, gloomy dungeon, and go to TPP to feel the liberation of the clean air as you come outside).
Music, absolutely. I'd say music is about 1/5th contribution to immersion, and good, fitting music really helps to "glue" you to a game. You could extend that to sound design generally. For example poorly cloned footsteps can ruin immersion, whereas properly varied footsteps help.
Art style definitely - though here there's a lot of leeway, it depends on the genre, sometimes a more cartooney or less realistic art style can be fine. But if you're going for a proper feeling of apprehension and doom, realistic and/or gothic (and or alien in some sense) is the way to go.
High lethality. Definitely. You should be on the same level as the mobs, none of this bullet sponge nonsense (except where appropriate ofc, with monstrous bosses, etc.).
Reactivity. Definitely, the more the world responds to whatever random probing of it you decide to do, the more immersive it is.
As always, I'd be careful to distinguish several things. There's "immersion" in the sense of the feeling of "being there" in another world, in the virtual world as depicted (the acute version of it is called "presence" by analysts, it only happens rarely but you'll know it when it happens) - part of one's brain forgets that one is a geek sitting in a Herman Miller, and one feels transported to this other place. Related to that is "immersion" in the sense of roleplay, in the sense of being or acting your character in that virtual world (this has a lot to do with C&C); I suppose that's straightforwardly called "roleplaying." Then there's "immersion" in the gameplay itself, which I think is more properly called "engagement," the feeling of being in a trance state, where your mind is thoroughly absorbed by the gameplay - by making your build, by going over your options in combat, or by developing good twitch skills and "throwing shapes" as you're playing, so to speak. In general, being absorbed in finding the optimum, most elegant path to success or victory.