The Death Busters are aliens from the Tau star system. When their home exploded, they took the remnants of their star system and went searching for a new home. They brought with them their source of power, the Taioron Crystal.
They found the perfect place to call their new home: a green-blue planet, full of life and potential (i.e., food.) -- the planet Earth. The fact that Earth was already inhabited did not faze them; they planned to feed on the humans' souls and use their bodies as vessels of power. Besides, Pharaoh 90 (the powerful, amorphous leader of the Death Busters) could not visit Earth; he needed Mistress 9 to open the doorway for him.
Meanwhile, a brilliant, amoral scientist named Professor Tomoe Souichi had been recently expelled from the academic community. A fire had taken his wife and injured his daughter Hotaru; he was busy rebuilding her body when a bolt of lightning struck near him, hitting his assistant Kaoli. It was the doing of the Death Busters; they took over Kaoli's soul, making her Magus Kaolinite, servant of Pharoah 90. They also gave Professor Tomoe eggs of daimons, the seeds of the Death Buster invasion. Tomoe inserted a particular daimon egg into the body of his daughter - the seed which would give her body to Mistress 9.
The Death Busters established themselves in the Mugen (Infinity) Zone, building an elite school called Mugen Gakuen (Infinity School) to draw talented young souls; these souls would feed Pharoah 90's growing power. These unfortunate children would also become vessels for daimons. With the help of the Witches 5, the Death Busters fought the Sailor senshi and built a power base on Earth.
The only thing that the Death Busters feared was the coming together of the three talismans. If the three talismans came together, it would mean the ruin of the Death Busters. Nothing else could stop them.
Personally, I think that they are the best enemies of the entire series. They have a plausible identity, a logical mission, and are pretty darn near unstoppable. They had a good plan, too; they established a very secure power base, and managed to lure many people to their cause. If they'd picked another mad scientist - if Sailorsaturn hadn't been in Hotaru's body - then all would have been lost. Everybody's attacks, including Supersailormoon's most powerful, were ineffective against them. Of the other enemies, Beryl was driven by lust, and Neherenia by revenge; Nemesis was just weird, and Galaxia's plain crazy. Pharoah 90 and Mistress 9 are aliens who just want food and a place to live. What's not to like?