Maxwell Forrest was a Human Starfleet official in charge of the NX Project during the 2140s and 2150s. As a commodore, he supervised the first tests of the warp five engine. As such, he worked closely with the Vulcans, who were supervising Humanity's progress into space.
As a Starfleet Commodore, Forrest was responsible for overseeing the NX Project and had been doing so as early as 2143. In that year, he would choose A.G. Robinson over Jonathan Archer to pilot the NX-Alpha. This decision was a difficult one for Forrest since the engine of the NX-Alpha was designed by Archer's father, Henry Archer.
Robinson easily broke the Warp 2 barrier, but the ship exploded shortly after reaching warp 2.2. Robinson survived by jettisoning an escape pod while at warp. The Vulcans claimed that the warp program should be postponed. Forrest stopped at the 602 Club, a bar frequented by Starfleet personnel, and informed Archer and Robinson that the program would be suspended. After Archer and Robinson disobeyed orders and ran a new test that was successful, Forrest persuaded Starfleet Command to reinstate the program. (ENT: "First Flight")
The Enterprise mission
As an admiral, Forrest was responsible for supervising the ongoing mission of the Enterprise NX-01. After a Klingon crashed on Earth, the Vulcans wanted to delay the mission and return the Klingon to its homeworld. Forrest overruled them and decided that Starfleet would return the Klingon. He authorized the early launch of Enterprise to return Klaang to Qo'noS alive despite the protests of Ambassador Soval and the Vulcans.
Jonathan Archer, son of Henry Archer, who had designed the warp engine, was assigned as the captain of Enterprise. Forrest told Archer that Humanity had been waiting a hundred years for this chance, and told him not to screw up. Forrest also officiated over the launching ceremony of Enterprise. At a press conference prior to the mission launch, he said that Humans had been ankle deep in space travel and that it was time to swim. (ENT: "Broken Bow")
Forrest stayed in constant touch with Enterprise. He gave many orders as different situations arose.
He ordered the ship to investigate a distress call from ECS Fortunate, a cargo ship that was attacked by Nausicaan pirates. Enterprise was visited by a group of Vulcans who did not embrace logic. Forrest contacted Archer and asked him to have one of the Vulcans, named Kov, call his father, who was dying. (ENT: "Fortunate Son", "Fusion")
Forrest had to constantly walk a delicate balance between the goal of Human space exploration and Vulcan misgivings about it. After the discovery of P'Jem as a base for spy activity against the Andorians, it was destroyed in an attack by the Andorians. The Vulcan High Command called for an end of Enterprise's mission. When Forrest refused, the Vulcans called off joint Earth-Vulcan fleet operations and wanted T'Pol transferred off Enterprise. The Vulcans eventually relented after T'Pol and Archer saved Sopek, a senior Vulcan officer. Later Forrest would order Archer to arbitrate a dispute between the Andorians and Vulcans after hostilities broke out over the disputed planet called Weytahn. He also ordered Enterprise to transport Vulcan Ambassador V'Lar from the Mazarite homeworld. She had information on the corruption of government officials and her life was in danger. (ENT: "Shadows of P'Jem", "Cease Fire", "Fallen Hero")
After an accident seemingly caused by Enterprise killed 3,600 Paraagans when tetrazine was ignited by the ship, Forrest informed Archer that at the urging of the Vulcan High Command and Starfleet, Enterprise's mission was canceled. After Archer presented evidence that vindicated Enterprise, the mission was reinstated by Forrest. (ENT: "Shockwave", "Shockwave, Part II")
After Archer contacted him about a strange space ship with a Human corpse in it. Forrest thought that it might be Zefram Cochrane who had disappeared mysteriously. (ENT: "Future Tense") After an arctic team lost contact with Starfleet, Admiral Forrest was informed and led a team to investigate. They rushed to the site, only to find it abandoned. He found that the scientists were missing, as was their transport. Admiral Forrest called in Enterprise to find the transport. This was Humanity's first contact with the cybernetic beings known as the Borg, although they never found out what their name was. (ENT: "Regeneration")
The Xindi mission
After the first Xindi attack and Archer's meeting with the humanoid from the future who gave him details of the Xindi, Forrest meets with Archer at Starfleet Headquarters. At first, Admiral Forrest was not convinced about Archer's information. Forrest wasn't convinced that Archer's information justified a mission into the Delphic Expanse. After Archer provided proof by proving that the remains of the Xindi probe which shows that some of the debris was from the future, Forrest authorized the mission. (ENT: "The Expanse")
After the successful Xindi mission, Forrest welcomed the Enterprise crew home as heroes. Archer was debriefed by Starfleet Command and the Vulcan High Command. When Ambassador Soval insinuated that the trellium-infected Vulcan ship Seleya was destroyed without doing enough to help the crew, Archer became outraged, blaming the Vulcan High Command for not providing enough assistance in their mission. Admiral Forrest ordered Archer to take some time off to clear his mind. (ENT: "Home")
Forrest was killed in 2154 in a terrorist bombing of Earth's embassy on Vulcan. In his final conversation with Ambassador Soval, he was discussing joint missions between Earth and Vulcan. Forrest's last act was to push Soval out of the blast wave, sacrificing himself. (ENT: "The Forge")
In an alternate timeline, Forrest sent a message to Enterprise after meeting with the Command Council to transfer command of the ship to Subcommander T'Pol. He was likely killed when the Xindi superweapon was deployed against Earth shortly thereafter. (ENT: "Twilight")
In a character breakdown sheet that Paramount sent to various talent agents upon casting Star Trek: Enterprise pilot "Broken Bow", Admiral Forrest was described as a non-recurring role, scheduled to appear only in the pilot episode, and was characterized thus; "Human male. 50s to 60s. A career military man who's the highest ranking officer in Starfleet. He's fond of Captain Archer and has personally selected him to command Enterprise."  Forrest was played by Star Trek veteran Vaughn Armstrong.