Conflict Zones spawn in systems where at least two minor factions are at war with each other (Faction states War and Civil War). They typically spawn in open space, but in a close orbit around planetary bodies. Three intensity classifications exist, High, Medium and Low. Upon entering a conflict zone, the player is asked to join one of the two factions at war.
Winning the conflict zone is achieved by reaching more points than the opposing faction, indicated by two colored bars. Points are gained for enemy ship destructions, and by completing a set of tasks given to the player. Completing a CZ is the only way to influence the outcome of a war between minor factions.
A Low CZ is just regular enemy ships, albeit with better builds than pirates. They are a bit more difficult than your standard HazRes. Player ships with minimal engineering can usually handle these fine.
A Med CZ has ships that are a bit tougher. A medium can also spawn special ships that give a bonus payment to kill or escort, depending on their faction in the conflict. These can include a captain to escort/kill, correspondents to escort/kill, and Spec Ops. Spec Ops can punish the unprepared commander, whether new or seasoned, because their ships are far tougher, and their weapons are engineered. There are always four Spec Ops ships: Alpha, Beta, Gamma, and Delta. Spec Ops and Captains can be identified from distance by the fact that they are the only NPC ships that use colored weapons.
A High has even tougher ships, the same special ships, and can spawn capital ships if the Federation or Empire are involved, but that doesn't always happen. Generally, if Spec Ops spawns in a high, the capital ship won't, and vice versa. A capital ship is defeated by destroying its heat relays, located by targeting the ship and cycling through sub targets. Destroying all heat relays will force the capital ship to flee (they cannot be killed). Highs are quite a bit tougher than lows, and generally require a decently engineered ship, or a wing of other players.
A Powerplay Conflict zone, currently (2024 December) only in the Medium variety, is just like the above "BGS" Medium, but is part of Powerplay leaders vying for control of a system. The credits are perhaps worse but the powerplay merits are good.
Note: The special ships and/or capital ships are NOT required targets to win a CZ, but they do help.