Star Wars Episode 0: The Requel
The Jedi are an ancient religious organization serving as the self-proclaimed guardians of peace and justice in the galaxy. Functionally, they are usually an arm of the Galactic Senate, sent on peacekeeping missions and various kinds of special operations.
Most people have vague unease around Jedi, as they are seen as anachronistic, and not everyone has forgotten that they have dragged the galaxy into war on at least three or four occasions. Their opponents have been one of their own sects, called the Sith, though that is not a word that most people remember.
The most active (read: meddlesome) Jedi are the Jedi Knights, tasked by the High Council or by other Jedi Masters with maintaining Jedi influence in the galaxy.
The full Jedi Code is lengthy and often-amended over the millennia, but can be summed up as the following:
There is no emotion, there is peace.
There is no ignorance, there is knowledge.
There is no passion, there is serenity.
There is no chaos, there is harmony.
There is no death, there is the Force.
In theory, they are supposed to be peacekeepers and justicars, fighting for the innocent and taking vows of poverty. In practice, the view from the outside is that they are hardly so high-minded.