[The following is a companion piece to a larger work, titled "Is Game Music All It Can Be?" I suggest you read that one first.]
The leitmotif is a concept that was really exemplified by Richard Wagner, the famous opera writer of the late Romantic period. You can read that link for a thorough explanation, but at its base level a leitmotif is a very small musical idea that serves to announce the presence of a character, place, object or even idea. Think of it as a mnemonic device of a story. It has become the one of the most important idea in scoring for feature works. Games, however, seemingly have no clue how to exploit this idea to deepen and enhance the player's experience.
“But wait!” you say. “I hear recurring themes in my games all the time!” Yes, it’s true, there are often common themes running through sequels, but this does not explore the full potential of the leitmotif. Wagner himself started out with this sort of unchanging theme, used over and over to the point where Claude Debussy said the use "suggests a world of harmless lunatics who present their visiting cards and shout their name in song." This is not, as you can imagine, the kind of image you want to project.
