Imagine a game that you have played from beginning to end or one that you have simply loved and played for a long time. Would you be able to write a two-to-five pages short presentation on that game? A presentation that describes why is it fun, how you play it, what it looks like, and for what kind of player it isgoing to be a great experience?
Now imagine that you've never played that game, that it doesn't even exist yet. Would you still be able to describe it?
That vision is the game you want to make and the presentation is a game concept.
The purpose of the game concept is to describe a game with enough detail to distill and communicate its vision to the reader. To explain what makes it fun, who'll enjoy playing it, and why we should make it a reality.
One of the main responsibilities of every game designer is to make sure that, at every stage of development, the vision behind the game is clearly documented and communicated to the team.