A Jurisdiction is the area controlled by a minor faction. The minor faction which controls a jurisdiction issue fines and bounties for crimes committed there, determine who is wanted, and what cargo is illegal.
The jurisdiction in a system is determined by the systems controlling faction. This extends to all areas outside of the local space around a station, or outpost.
The jurisdiction of non-supercruise space around a station or outpost is that of the station or outposts controlling faction. This means that if you are wanted by the controlling faction of a system, you may find that you are not wanted when at the station of another minor faction, even in the same system.