The Companion was a female energy-based lifeform, originating from an alternate universe devoid of stars. She saved Zefram Cochrane's life when he would have died in space, and rejuvenated his body, keeping him alive far beyond his natural lifespan. She fell in love with him.
When the crew of the USS Enterprise found the two of them on the planet, they tried to take Cochrane away from her. She resisted this, and attempted to keep the Enterprise landing party there as well. Captain Kirk and Spock attempted to kill her, but failed. Eventually, they convinced her that Cochrane would never love her, as she lacked a physical body. So, she merged with Nancy Hedford, a dying member of the landing party, a human woman. Cochrane willingly remained on the planet to marry her. (TOS episode: "Metamorphosis")
In 2268, she and Cochrane encountered the Enterprise crew again, who had stopped by for help discovering a way to recover hyperwarp ships which had gone missing near Gamma Caneris N. The Companion attempted to foil Kirk's attempts, knowing it would lead to the Enterprise's destruction. When Cochrane ignored her warnings and improved the Enterprise's engines anyway, The Companion left Nancy Hedford to protect the Enterprise as it accidentally entered the universe that the Companion's race originates from. There, the Companion's people, who had taken over the Hyper-Warp craft, demanded that the Companion stay or else they would destroy the Enterprise. But the Enterprise was able to escape before they were able to do anything using the hyperwarp modifications designed by Cochrane. The Companion then remerged with Hedford. (TOS comic: "A Warp in Space")
She died at the same time as Cochrane, a century later in May 2366, aboard the USS Enterprise. Captain Jean-Luc Picard agreed to position the ship so they could see the starfield they were familiar with. (ST novel: Federation)