High security systems, often shortened to 'High-sec', are systems that CONCORD actively patrols against illegal PvP by sending ships to any illegal occurrence of player-on-player fighting within the system. A high-sec system is any system with a security (sec) rating of 0.5-1.0. If a pilot commits and act of aggression while in high-sec systems CONCORD will respond with wave after wave of deadly force until the aggressor's ship is dead sparing the pod.
In some releases of EVE these waves could be tanked indefinitely with certain tactics. As of Revelations 2 this is impossible but the aggressor might last long enough to kill the target of their illegal aggression. This tactic is used by some pirates, see suicide ganking.