She resembles a four-armed moth or similar insect, but without visible wings, instead levitating with what appear to be vestigial legs. She makes a ghastly snarl when moving around and a frightful shriek like a Banshee when she is attacked.
The Mother Demon's attack consists of powerful flame trails, followed by a set of four homing fireballs which split up when when they strike a target.
The Mother Demon is said to have escaped detection in the original campaigns somewhere in a base on Mars or its moons. After many years of an absolute quarantine guaranteed by massive levels of radiation, an old relay satellite, battered by neutrons, suddenly activated and broadcast a message containing information about the Mother Demon and her progress toward resurrection of the other demons via her vast powers of rejuvenation.
The Mother Demon will kill you quickly if you come into the battle unprepared. Her flame trail, when hit, launches you into the air in a manner resembling the attack of the arch-vile, making it difficult to control your movements. At the same time, she will launch four homing rockets at you. Even though a single missile is not as strong as a cyberdemon's rocket, getting hit by all four of them at once can be fatal regardless of your health and armor levels. Dodging the rockets can be a hassle, especially when hit by the flame trails. Beware of the homing rockets even if dodged, however, as when they explode they will send out a barrage of smaller fireballs in all directions.
The most effective way to defeat the Mother Demon is to use the fully-equipped Unmaker at point-blank range. Not only will the Unmaker do a lot of damage at rapid-firing speeds, but will also stun her to prevent her from using her 4 homing missiles. She will still attack with the flame trails as the only attack to avoid. Under suppressed fire from the weapon, she will go down in no time. Her attacks are surprisingly ineffective at short range, the homing missiles flying past her target and usually striking a nearby support column.
If you did not retrieve all three of the Demon Keys needed to fully equip the Unmaker, the battle against the Mother Demon will be significantly more difficult, both due to the Unmaker being less effective, and because lacking the keys means needing to fight a large number of monsters before the Mother Demon will emerge, using up much of your precious ammo. Your only real choice in this situation is to use the BFG 9000, but it requires precise timing and enough plasma cells conserved through the previous battle against the horde of enemies. The rocket launcher is the next best alternative.
In Doom 3 Resurrection of Evil, when you bring the stone artifact to the scientist for scanning, during his conversation with Dr. Elizabeth McNeil, a stone tablet bearing an image of the Helltime Hunter can be seen which appears strangely similar to the Mother Demon.
The final boss of Half-Life, Nihilanth, greatly resembles Mother Demon. Like Mother Demon, Nihilanth has multiple arms, vestigial legs and an oversized head, and attacks with volleys of homing projectiles.
The Mother Demon in the Doom 64 TC.