(covers information from several alternate timelines)
The Command Council was a group of high-ranking Starfleet officers in the 22nd century, responsible for the oversight of the missions of Starfleet vessels, including Enterprise NX-01. Led by Admiral Maxwell Forrest, the Council decided on command assignments, and issued mission-specific orders to Starfleet Captains.
In 2152, Admiral Forrest called an emergency meeting of the Command Council upon the destruction of the Paraagan II mining colony, which was apparently caused by the Enterprise crew. Consulting with Vulcan ambassador Soval, the decision was ultimately made to cancel Enterprise's mission of exploration. However, upon acquisition of proof that the Suliban Cabal was actually responsible for the destruction of the colony, and had subsequently attempted to frame the Enterprise crew, the Council reversed its decision, and allowed the mission to continue. (ENT: "Shockwave", "Shockwave, Part II")
In an alternate timeline in 2153, the Command Council relieved Captain Archer of duty as captain of Enterprise, upon reviewing Doctor Phlox's report on Archer's infection by a series of parasites which inhibited his ability to form new, long-term memories. The timeline in which these events occurred was negated twelve years later, when a subspace implosion neutralized the parasites in all time periods, changing history in such a way as the infection never occurred. (ENT: "Twilight")
In 2154, the Command Council debriefed Captain Archer upon the completion of Enterprise's mission in the Delphic Expanse, in which the Enterprise crew successfully prevented the Xindi from launching an attack meant to destroy Earth. Upon the conclusion, the Council ordered all details of the debriefing classified. (ENT: "Home")