Nebulae are scattered around the map, the number determined by map size, if any players are Normal+Champion or Extra Champion.
Nebulae are not planets in any respect.
These may only be accessed with champion ships, require a lot of attention from their controlling player, and provide a reward upon completion.
All nebulae give your champion experience points, which may be spent to unlock higher-mark versions of modules and 500 knowledge. All nebulae also give fabricators, which each allow you to build 7 starships and give an economic reward.
The second nebula completed gives you the destroyer hull size. The fifth nebula completed gives you the cruiser hull size. The ninth nebula gets the battleship.
The first time you complete a nebula for a new alien group (zenith, spire, neinzul), you receive the associated champion hull and modular fortress.
Completing nebulae before increasing AIP will result in the AI Homeworlds having additional nemesis champions (frigate size, minimum of 6, maximum of 20). These can significantly increase the difficulty of the final assaults.