Dark Matter is used to permanently boost your ship stats, by purchasing permanent upgrades for your Missiles damage, MG damage, Tech damage, Hull health, Credit drop and Dark Matter drop.
Dark Matter is mainly gained through the Dimension Jump, or alternatively through purchaseable bundles or free ad chests. The Dark Matter obtained depends from the progress you made before jumping: the more bosses you fought on the way, the more Dark Matter. Furthermore, there is a multiplier applying on top of the Dark Matter, depending on the sector you reached before jumping into another dimension.
A Dimension Jump sends your ship into another dimension to Sector 1, resetting all temporary upgrades of your ship but rewarding you with the collection of Dark Matter and up to 4 Hyper Drives per jump.