All this data is potentially out of date, and should be taken with a truckload of salt
High security space (also referred to as Highsec and High-Sec) is systems with a security rating of 1.0 down to 0.5. These systems are policed by CONCORD which awards some safety from pirates. While CONCORD does not prevent acts of piracy in high security space, they will quickly respond to such acts and punish the perpetrator. In many cases the response time is fast enough to save the victim from destruction. They will also punish the act by adjusting the security rating according to how high the security in the system is, the higher the system, the higher the penalty.
Control Towers may only be anchored in systems with 0.7 or lower security. In addition to normal fuel requirements, towers in high security space also requires Starbase Charters in order to run. Anchoring may only be done by corporations with sufficient standing towards the Empire that controls the space.
Asteroid belt ores
0.7 - 0.5 system belts in Amarr space contain Kernite, in Caldari space they contain Plagioclase, in Gallente and Minmatar space they contain Omber. These ores are in addition to higher security ores above. Ice belts may be found in these systems aswell.
Belts in high security space usually only contains NPC pirates of Frigate and occasionally Destroyer size. Systems with 1.0 or 0.9 security have no NPC pirates.