In game, Deep Space (by-default) is viewed as the black regions of space. These regions spawn celestial bodies with three different biome types - Ice, Lava, & Wasteland. This region can spawn the highest level of celestial bodies, up to level 9! The planets which spawn in this region can also be upgraded 5 times (the most of any space-type, along with Dead Space).
The colouration of the background where Deep Space is the Space-Type (fancy-shaders on)
A peek at the variety/design of biomes which can spawn within Deep Space - Ice, Lava & Wasteland!
It is within Deep Space that players spend the majority of their time when playing a round due to the nature of the stats of the celestial bodies which spawn here. The defense is low when compared to Nebula & Space, just a quarter of the same-level values, however all other stats are high - 50% higher than Nebula, and 20% higher than Space. This region is where a player can truly begin to amass a terrifying empire by capturing large planets, finding up to maximum rarity artifacts, and project force towards other nearby players. The lowered defense means that your attacks often do bonus damage when landing on an enemies celestial body (read about Defense for more information).
As you continue to expand, you will begin to look to the last region of space, Dead Space, for specific reasons (if you see a super high level planet, foundry or celestial body of note). However since Deep Space generally covers a lot more of the universe, it is where many of your most powerful celestial bodies will reside.