The Grey Jedi are an order of Loopers who broke off from the Jedi due to differences in opinions about multiple issues as well as the fact that they scared the shit out of the majority of the Non-Looping Jedi masters.
They are known as Grey Jedi because they are more impulsive and pragmatic than "Light" Jedi, seeing no problem with using "underhanded" tactics to give them the win if the situation calls for it. They also stay in tune with their emotions rather than the detached enlightenment that Jedi strive for.
That being said the Grey Jedi are by no means Sith. They do not fall prey to their emotions, and generally understand that with power comes the possibility of abusing that power and all the terror that such events bring.
The order was first founded by the Original Seven, as well as any Loopers such as Sasuke Uchiha and Sakura Haruno. They would continuously "refound" the order whenever they would Loop back into the Star Wars Loop.
While it is unmentioned if other Loopers are official members of the order, quite a few agree with at least some of their ideals. Twilight Sparkle, for example, has gone against the Jedi on their stance against Love, sighting the near innumerable marriages and children from those marriages as proof for the dissolution of the Love Restriction.
The Grey Jedi as a concept were later shown to still exist as a set of guildline and instructions created by Luke Skywalker and several O7 members through trial and error, known as the Grey Jedi Initiative.