Immersion is the primary goal of any game. You play to get away of the real world for a little, catch a break. When in immersion is achieved in a virtual world, you feel like you are actually there. Some examples that amazed me:
Running in Battlefield 3. The character breathes like a real person while running, camera shakes in such a way that it looks just like if you were sprinting. The detail of the surfaces looks so real. Then you suddenly find a jeep and get on it thinking "man, good thing I found a jeep, I was getting tired of running". But you were not really running, you are sitting in a computer... that's immersion.
Raining in Minecraft. Specially using surround sound. You stand inside your house during a rain. Looking out the door, you year the rain. You turn around and now you hear the rain behind you. You turn around again, you hear the rain in front of you... you get out into the rain, it sounds louder now and suddenly you feel cold. You actually feel cold, because rain is falling on you... but you are not really in the rain, you are in front of a computer... that's immersion.