Quoted from WaddleJrJr:

Taking the assets of the game's theme and implementing them into gameplay in a way that makes you actually feel involved with whatever the theme is.
The best example I can think of is America's Most Haunted. AMH uses the balls and toys in very innovative ways, to make each ball feel like a character in a story. For example, in the doctor mode, one of your fellow ghost hunters gets trapped in the morgue with the doctor ghost (this is shown on the playfield by the ball getting trapped in saucer behind the door). Another ball is launched out (you) as you try to save your friend. You bash the ghost to distract him (the ghost toy then looks forward right at you and makes remarks directly to you the player), and then you hit the door to damage it while he's distracted. The ghost then snaps back to looking at the door and makes more comments. You repeat this process until you bust down the door, and as you're doing so your partner who is trapped in the morgue is making comments back at you. That's just illustrating one mode of the many in the game, and each integrates the theme and makes you feel involved with the game's story and world in similarly innovative ways.
So an example of a game in this thread that's been brought up a lot that I can't seem to find good theme integration in at all, Tron. What about the features in Tron have anything to do with the Tron element they're suppose to represent? Like if Quorra multiball didn't say Quorra on it, how would you know it has anything to do with the character Quorra? You're not interacting with the game in any special way that relates to the character, you're just playing a multiball. I find all the modes/multiballs in Tron to be similarly detached from the theme. Don't get me wrong, Tron is an incredible game, I just can't find any way that it represents the qualities of good theme integration.