Reputation branches into two sections- Behavior and Social. Social Reputation regards your interactions with the inmates and employees of the jail and is useful for reasons that will be explained later. Behavior Reputation measures if you are a Good or Bad inmate, and like Social, it is useful for many reasons.
Reputation with your fellow inmates is paritcularly important, because with a moderate Strength rate, you can racket the inmates for credits (Or food, if chosen in a seperate option). Having a bad reputation with the inmates is bad in itself, because you may find yourself killed. Once you attain the rank of Don, you will be treated like a ruler with the inmates, and if you racket food from them, they will arrange a special feast for you.
Having a good reputation with the guards is not easily achieved, but essential for any goody two-shoes that got into a slight altercation with the law. Usually, deciding to be friends with the guards means you will have a low reputation with your inmates, and that might mean death. With a Good Behavior Reputation, you can be released on parole. (Parole is nothing like real parole, as it has no effect on the game and no violations are existant.)
Behavior reputation is like Social Reputation, because it affects your standing with the two major groups. Having a Bad behavior means you might get an extended stay in the jail, and you might find yourself included with the guards more often. Having a Bad reputation also means inmates will respect you more. Having a Good reputation means that you might be finding yourself in trouble with your cellmates, rather than the guards. Having a Good reputation is crucial for being released early.