The Moderator / Moderators (they have been referred to as singular or plural on instances) are a mysterious collective of intergalactic guardians in the universe of the Kampfer anime series. They are the behind-the-scenes main antagonist of the series.
Their / its number(s), species, true appearance, and powers are unknown. It is also unknown how they first contacted Kaede Sakura-san, and whether or not they have any other people like Kaede who act as their avatars and cause the changes of their colleagues into Kampfers.
Before the Series
During the Red/Blue Galactic War, the Moderators were selected as an independent peacekeeping agent. Their plan involved stopping the war between the Red Force and the Blue Force by having others fight for them as their pawns, known as the Kampfers. Peace would exist between the red and blue force as long as the Kampfers continue to fight for whichever side they are selected to be in.
The Moderators give their chosen people, usually women, superhuman strength and agility, as well as cause their physical forms to be altered and give them the ability to magically produce a specific type of weapon. Red an Blue Kampfers are chosen and imprinted with the knowledge that they have to fight and kill members of the other side, with no explaination about why.
To enable their chosen to become Kampfers, The Moderators needed an avatar on Earth, a human through which they could implant their consciousness and enforce their will. Their choice was Kaede Sakura-san, who was imprinted with an obsession for the kinds of dolls that the Moderators gave out as Guardians to their Kampfers, and ordered to give them to people in her circle of The Moderators' choice. In return for her unwitting service, Kaede was given exceptional swordsmanship abilities, as well as invulnerability and immortality, though at the present Kaede is utterly unaware of this when not being used as an avatar.
The Guardians take the form of disemboweled animal dolls, which are able to talk to and guide their respective Kampfers.
The White Kampfers
After Shizuku-sando refused to kill people she didn't know for a war that neither she nor her other side knew anything about, she allied herself with the blue kampfers Seno Natsuru and Akame Mishima, the Red/Blue Galactic War was thrown out of balance, and the Galaxy was at risk of total chaos. Resultantly, The Moderators used Kaede to create an army of new warriors, called the White Kampfers, which were total slaves to Kaede's will (and, by extension, The Moderator's will), in order to kill the rebellious Red and Blue Kampfers.
While never seen on screen, their personality can be observed when they use Kaede's body as a vessel towards the end of the series. When expressing themselves in this way, the Moderators show themselves to be sadistic, manipulative, trash-talking, and willing to take advantage of any of their opponents weaknesses. They are also willing to kill anyone who stands in the way of their agenda to prevent the re-eruption of the Red/Blue Galactic War, but it is shown in Episode 1 of Kampfer Fur Die Liebe (through Kaede's actions) that they blieve in a fair fight, and that if their enemy at any point lets their pawns live, they will let their enemy survive their next battle as a return of the favor, suggesting that they have a code of honour of some kind.
However, they are not above mind-controlling people into a bizarre form of willing slavery (e.g. the White Kampfers), and (based on Kaede's actions as their avatar) seem to relish the idea of causing their enemies as much psychological, sexual, and emotional torment as it is possible to give them.
The Moderators are extremely similar to another organisation, The Guild, from the anime series Last Exile, as both groups are associated with the colour white, both keep peace between opposing armies during a conflict, and both will employ any means that they see fit to ensure that the conflict does not sway in any particular direction, and impose rules on either side.