The Supernova is a game event that occurs after 20 minutes of playing the game. After 20 minutes, the Sun will shrink to a point and then explode outwards, casting beautiful rays of light everywhere. It expands outward and kills you.
The expansion accelerates, making it impossible to outrun.
In the final 60 seconds of the system cycle before the Sun goes Supernova, a distinct song will play that is only heard in this final minute of the 20 minute cycle timer, and is heard wherever you are in the game. Upon the song finishing, the Sun will go Supernova.
Physics (if any)
A supernova is a large cosmic event which occurs when the core of a star begins to fuse heavier and heavier elements, eventually creating iron and running out of fuel completely. This results in the star collapsing in on itself, exploding outwards with what should be a bang, but is in fact a disappointingly silent explosion. But this is a game, thus, there is a bang.
Unfortunately, assuming that the sun's shockwave travels at the speed of light, (about 300 million m/s) there is no way to outrun the supernova in Outer Wilds. Your ship accelerates at roughly 100 m/s^2, meaning it would take just less than 35 (34.7) days real-time of constant acceleration to match the speed of the supernova. Seeing as you only have 20 minutes until the supernova, it is only possible to accelerate to 120,000 m/s; far less than the required speed.