According to the Doom Manual, Deimos is used to store nuclear waste, and is also the home of teleportation experimentation with Phobos. Sometime before the game however, an experiment goes wrong, Deimos vanishes, and the Phobos base is attacked by an unknown force, and the player's squad is sent up to investigate.
By the time the Lone Marine crossed over to Deimos, he found the human personnel there slain or transformed into zombies, and the complex was now under the command of a Cyberdemon and its minions, who were gradually transforming the advanced facilities built there by humans into a grim bastion of great evil. However, the Marine was able to battle his way to the Cyberdemon's lair at the Tower of Babel, and destroyed its infernal master, avenging the loss of human life on the moon station.
Deimos isn't shown physically in the fly-in in the intro, however it's orbiting projection is shown under Phobos.
Behind the Scenes
In Doom Deimos is represented as having older style bases (barring the presence of Hell corruption) composed of Brick, and Cement walls, the shape of the Deimos is notably square compared to the abstract-design of the Phobos, and Inferno levels. Deimos is also represented as having large brown mountains capped with small amounts of snow, despite the intermission screen showing a grey landscape, similar to how Phobos is shown having large grey mountains covered in vegetation, but a brown cratered landscape in the intermission screen, and in levels.
In reality, Deimos is much smaller than Phobos, only having a radius of 6.2 kilometers, possess little gravity, and no atmosphere (even if it had an atmosphere, it would drift off without some form of Artificial Gravity technology).