The Jedi Covenant was a secret organization of Jedi founded by former Jedi Master Krynda Draay. Based on Coruscant, the Covenant's focus was to seek out any shatterpoints in the Force that could ultimately result in the resurrection of the Sith and negate or otherwise remove them, by any means necessary.
Sometime after the Great Sith War Jedi Master Krynda Draay, having assumed personal responsibility for the Great Sith War by not sensing the changes in Exar Kun before his fall to the dark side, established a small and secret organization made up primarily of Jedi Consulars (force users most adept at reading the currents of the Force and seeing visions of the future) and Jedi Shadows (force users who act unobserved and carry out their tasks unseen).
In order to help Krynda with some of the more mundane tasks of the Covenant - maintaining the Draay Estate and its Trust chief among them - she employed the help of her deceased husband Barrison's best friend Haazen to assist her. A failed Jedi Padawan and longtime retainer of the Draay family, Haazen served as Krynda's personal aide and acted as relay between Krynda and the rest of the Covenant.
The Covenant itself consisted of several groups of Jedi Consulars that were grouped into WatchCircles, each established with the purpose of specializing in a specific precognitive field. Each of the WatchCircles was made up of four Jedi Consulars who would act as the seers and precognitives, while a fifth member - typically a Jedi Guardian - would serve as the "hand" or "executor" and would both direct the actions of the individual WatchCircle as well as report their findings to Haazen, in his unofficial capacity as "hand" of the Covenant itself.
In addition to the WatchCircles, the Covenant also had in its employ several Jedi Shadows that were tasked as field agents, sent to retrieve Sith artifacts as well as investigate shatterpoints and other nexuses of Force energy.