The first, and perhaps the most obvious, is that it "reels in" your wild ideas and gives you a clear idea of how the world, characters, and plot you're writing operates. If a character has a backstory, it can greatly enhance your idea of how to write one's motivations- even when it's not stated in the plot. (For a great example, see Iago from Shakespeare's Othello).
Here are a few character backstories I made up on the spot from famous videogames:
1. Duke Nukem is a man with a troubled past. His father died when he was 10 shortly after he divorced his mother for sleeping with other men. He dealt with his turmoil by adopting an ultra-manly attitude, illusions of grandeur, and a womanizing attitude. As an adult, he was given great opportunities to succeed in the Earth Defense Force, where his self-gratifying behavior enabled him to kill many of his enemies without the moral problems of other men in his unit. Soon later, his actions in stopping the evil plots of the criminal mastermind Dr. Pluton, as well as thwarting invasion and abducion attempts of alien varieties helped him cope with the loss of his father, but further prevented him from ever becoming stable, and this only pushed him further towards defending the earth.
Now imagine if this was the true backstory for the Duke Nukem 3D games. Notice here that it gives the game some sort of validity in terms of its plot and overall narrative, and how it clearly sets in the player's mind that Duke's self-gratifying personality is a part of his troubled past. The game clearly gives no origin story for duke, but perhaps something similar was imagined in order to assist the developer's creation of their character, his goals, and his struggles.
2. Pong is a simplified representation of a tennis match where at any moment, one wrong move can ensure your failure. Except it isn't really about pong at all; it's about two scientists bouncing electrons back and forth in order to ensure their survival after a cataclysmic meltdown. Neither scientist wishes for his side of the security doors blocking exits to the two sides of the reactor, and thus their game goes on until the other gets deatomized.
This is perhaps the most unneccessary backstory here, but it serves as a reminder that a good sense of time and place can greatly enhance one's interest of the game, story, or other form of media a person is experiencing.
As you can see, even basic backstories can give new meaning for otherwise bland forms of media with little to no emotional content besides that of base excitement. Backstory is a very important part of the proccess of creating a story, a character, or a story's world, and should never be avoided even if it has no relation to what you are portraying in one's creation.