I'm going to do my best to keep this as spoiler-free as possible, but if you've played Until Dawn, the interactive drama horror game for Playstation 4 centred around five teens attempting to survive the night in a remote location in the mountains, then you should already know vaguely what to expect.
The Quarry is a "survival horror interactive drama" played from the third-person perspective of nine teenage camp counsellors, as they try to make it through the night at Hackett's Quarry.
Supermassive Games have themselves stated that they view this game as a spiritual successor to Until Dawn and so, much like it, The Quarry draws heavy inspiration from teen slasher movies - think Scream (1996), Cherry Falls (2000), or any of the Friday the 13th franchise.