Immersion is a somewhat nebulous concept that is subjectively defined, however it is an important concept in the development of games.  Initially, video games lacked the sophistication and technical capability to fully immerse the player in the game world.  For example, no one will ever confuse a game of Pong with anything that resembles reality, as it is flat, contains odd sounds, and lacks depth. 
 
 As games developed and technical capabilities increased, however, the potential for a fully immersive game experience developed.  Game developers began to use new graphical and story telling techniques to pull the player farther into the game world.  An early example of this is Myst for PC systems.  Myst used photorealistic, pre drawn backgrounds to give players a beautiful and detailed world to explore.  Myst also used a first person perspective, and offered players minimal instructions, helping to pull the player into the game. 
 
After this, however, immersion somewhat stalled as an important concept.  While games continued to improve, with better 3d graphics and sounds, there was little emphasis on increasing realism.  For example, Super Mario 64, a shining example of overall game design, technical capabilities, and almost universally well received, still always felt like a video game. The player was tasked with objectives such as obtaining enough "stars" to open new worlds, received tasks from Lakitus through scrolling speech, and fought Bowser by hitting him three times. 
 
Shortly thereafter a leap forward in immersion came from sports games.  Baseball, football, and hockey games all took major leaps on the Playstation and Saturn to improve their presentation.  This meant liscencing agreements with EPSN to use actual television graphics to display scores and stats.  Also, NHL games began dropping the health meter during player fights.  Football games began showing Jumbotron replays in-between downs.  Game reviews noted that these games were getting closer to watching the real thing. 
 
This development began to spread to other genres as well.  In the shooter genre, games such as SOCOM increased the level of realism.  SOCOM used highly technical terms to refer to weapons and military equipment, for example you did not obtain a "Rifle" but an M16.  Additionally, players could only carry limited equipment and ammo, as opposed to previous games where players could pull out seemingly endless weapons.  Also, there were no healthkits, and one or two bullets would completely incapacitate the player.  Finally, SOCOM asked the player to kill as few enemies as possible, in keeping with the real-world implications. 
 
Games such as RPGs began to see similar developments.  For example, Final Fantasy X developed a full world with a complete backstory, political tensions, and social mores.  Although the heavy emphasis on story is common in RPGs, FFX is a good example of the PS2 generation taking it further.  FFX, for example, reduced the HUD during random battles, making it appear that the player had simply run across dangerous monsters, rather than engaged in a strategy game.  Also, the mini game integration increased. Blitzball was created a sport, and NPCs would reference the sport throughout the game.  
 
In the current generation, this has reached new heights.  GTA4 is a good example of this.  In GTA4, the game world is fully developed to be a realistic and immersive city.  The city is gritty and dirty in places, much like in real life.  The player has a cell phone on which he can receive or make calls, and a computer that can actually access fake internet sites.  The radio plays both music and advertisements.  These all help pull the player into the game world, and, in a sense, forget he or she is playing a game.