Some general info about Psycho-Pass:
The show takes place in a future where technology has advanced enough such that a person's psychology and personality can be assessed and quantified in an instant. This technology has allowed the governing body to record and study such data to determine what constitutes a "good lifestyle" as determined by values. The measurement used to calculate the value of a person's mental self is known as "Psycho-Pass".
The tagline on the official site is "Justice will be dictated by the muzzle of this gun." But what's interesting is that the "gun muzzle" Kanji characters have an alternate reading above them in Katakana which says "system". So we can be pretty sure that those high tech guns the characters are using aren't the sort that are meant to shoot to kill. Instead they're probably part of an oppressive dystopian government technological system controlling society's standards.
Both lead characters revealed so far work for the Public Safety Bureau, but they're not partners working in the same department. Shinya is an enforcer in the criminal investigation department. The enforcers are the detectives who do the field work. Akane on the other hand is a rookie monitoring officer in the bureau. The monitoring officers are assigned to watch over enforcers.
It's a pretty typical set up for this sort of show, but it's so rare in anime these days. It seems likely that Shinya is going to "betray" the government organization at some point, and Akane will have to decide if she wants to call him in as a rogue or to trust in him because they have a bond. That's just an educated guess, but even if the relationship is predictable, I like these kind of stories.