The best games I have ever played, like the The Last of Us, have this incredible storyline that makes you feel every moment of it. Every heartache, every moment of joy, and every close call to death. There is no other game in my opinion that comes close enough to eclipse The Last Of Us by Naughty Dog. The story truly entrenches you in their world and makes you a part of it. You feel the pain of their loss, you feel their growing affection for other characters. You practically feel everything; the fear, the panic, and the excitement of delving through an apocalyptic world.
If the story is that good, you don't care where the story is leading you, all you can think about is how you want to see more of this world, you want to know what happens next. That's what really makes a game truly immersive and enjoyable to play.