Day Z isn't the most difficult game to explain to people at a functional level. It is a multiplayer survival game taking place over a large area of towns and forest populated by other players and zombies. Your character needs to stay healthy, warm and well fed in order to not die, and there are provisions, items and weapons littered around which can make survival easier. However once you get past that, to the 'why' of the game, things get confusing. There is no way to win; there is no guarantee of progress, no score system, no currency. In some ways this makes it one of the most challenging and creative games ever made. Not creative in the sense of the game design, but creative in the sense of how you play it - without imagination, without ideas and goals that you create for yourself the game has nothing. The game won’t tell you what you are supposed to want and you don’t even necessarily have to want to survive.
While the game grants you a huge degree of freedom it also lacks authority and with that long term consequences for actions. There is no automated police system and near-safe zones like you’ll find in EVE: Online; there is no system that simply blocks you from doing the same bad things to players as you would do to computer controlled enemies. You have a state of nature within the limitations prescribed by the game. (There are rules beyond the game, covering things like cheating, or certain gameplay options which depend on the server you’re playing on, but they're reliant upon being caught and the game admins opting to inflict a ban. Past that you’re on your own.)
The problem with freedom in the context of Day Z is that it is inevitable that players will turn on each other. There are simply not enough compelling reasons not to. In fact a lot of the mechanics of the game are actually geared towards helping people to turn on each other in creative ways. This is where things can get unpleasant. You can handcuff people. You can break people’s legs with axes. You can force them to eat tainted food or drink bleach. These are mechanics coded into the game with the presumed intention of making the game more fun for players.