Dunwall City Trials is a set of 10 challenges that will test your abilities that might not have been tested in the main game. There are four challenge types, which are Mobility, Stealth, Action and Puzzle. Your score is evaluated with a 3-star rating and you will unlock a piece of artwork for each star you acquire.
In order to get a single star on any challenge, you will need 10,000 points. Two stars requires 20,000 points and three stars requires a total of 30,000 points. Some challenges have an Expert version that unlocks upon getting two stars (so, 20,000 points). These Expert versions usually have something that differentiates it from the regular one, like not having use of abilities, as an example.