There are Captains. There are 1st Officers. There are even 4th Officers, all performing heroic stuff and adventuring in away teams. And then there are Privates. Those who clean the toilets. Those who provide cannon fodder for alien fire. Those who do the jobs no officer wants to. This is their game.
In Privates you play soldiers of lowest rank in a spaceship. You encounter aliens and oddities while cleaning toilets and guarding doors. Completing (unintentional) missions gives you prestige points, which eventually lead to promotion. The aim of the game is just that: to get promoted.