In our continuing efforts to keep H1Z1 a fun and safe place to play, we are introducing BattlEye to H1Z1. This service is in use with several other games and provides some unique capabilities that should have a noticeable effect in keeping cheaters out of the game, and should complement our existing anti-cheat features nicely. Any anti-cheat system requires continuous upkeep and we will keep modifying ours to provide the most level playing field possible.

If you wish to know more about BattlEye you can visit their site here. If you are encountering issues with BattlEye it’s generally a firewall preventing the program. Check that and their official FAQ first.
Source: Reddit