Mars (aka Risi Soru the Red Planet) is the fourth planet from the sun in the Solar System.
No action takes place on Mars itself.
According to the backstory the Marine of Doom II stopped an invasion at Mars Base which occurred over the course of a few days. He was the only survivor. He was sent home from Mars on shore leave only to discover that Earth was invaded after his drop pod landed.
In Doom 3, the action is set directly on Mars, in the UAC Mars Research Base and Mars City. The player is required to venture onto the barren surface of Mars a number of times during Doom 3, and must fight off demons while topping up their oxygen supply via collectible tanks. Although the planet is portrayed as being realistically inhospitable, a decision was made early on to increase Mars' gravity to match Earth's for gameplay reasons (in reality, Mars has barely 38% of Earth's gravity).
In this continuity, Mars was once inhabited by an advanced civilization that was destroyed by the forces of Hell after creating a teleportation device that led to the opening of a portal into the netherworld. The Martian race, in desperation, sacrificed their remaining population to create the Soul Cube which was then used by their champion in defeating the demons and sealing the portal to Hell. The few survivors left Mars and are implied to have traveled to Earth, where they became ancestors of modern humankind.
The backstory treats it as a sequel to Doom 1-3 (or at least in the same timeline, the exact order is not clear), it is set in the Mars Outpost the oldest facility on Mars, older than the Mars City.
In Doom II RPG the main characters (a different set of characters from the character in the first game) transfer from Mars to go to the Lunar Outpost.
Deimos is missing from Mars skies which seems to be a nod to the events of the original Doom/Ultimate Doom.
See Mars (2016)