Story Points are tokens that you get in the game for playing out the relationships you define in the first phase of the game. For example, you can define that another character "makes you crazy" and get a few story points when you have a scene with them in which they frustrate you.
Story points can be turned into dice during the game when you are rolling to defeat threat. You might, for example, turn in a story point to use an asset (like "A Swarm of Nanobots") to help you fix a broken airlock on your ship.
Story points are a huge part of the game and the Magpie Games issued ones are a perfect fit for your gaming table. They are lightweight, a nice size, and easy to toss around from player to player.