Big Mother is Marvel's adaptation of Grendel's Mother and is a mysterious creature that may be a demon or some kind mystical monster (though due to the nature of her summoning she is likely a demon, perhaps along the line of beings such as Lilith).
In 500 AD, in Denmark, the monster Grendel came to plague Heorot, the hall of Hrothgar, King of the Danes. Beowulf came to oppose Grendel and, when he returned to the king's hall, tore off one of his arms, apparently killing him.
Grendel's mother, enraged by the death of her son, emerged from her swamp and traveled to Heorot, dragging off and slaying Aeschere, a trusted advisor (and possibly the chief warrior) of Hrothgar. Beowulf tracked the mother back to her swamp, dove into her lair, and seemingly slew her using a god-forged sword.
It is later revealed that the mother of Grendel was not actually slain, but rather magically imprisoned in the ground below Denmark. Over the centuries, her prison migrated across the planet, until, in the modern era, it existed below Los Angeles, California.
Big Mother was freed from her imprisonment when Merlin Demonspawn spilled the blood of 100 virgins in his comic book store. Marlo Jones managed to talk Big Mother out of eating her employee Al. She then bought more time by starting a quarrel between Big Mother and Merlin.
The wizard wanted her to lead him to the Holy Grail which had been guarded by a dragon who was yet another of Beowulf's foes. However, Big Mother refused to be used by Merlin.
The two were about to fight when Merlin was attacked by Al wearing the armor of the Red Raven. Al was downed saving Marlo, but Captain Marvel arrived in time to engage Merlin.
Big Mother wandered out during the battle and briefly encountered Moondragon without incident.
She then encountered Rick Jones' former agent Mordecai Boggs. Boggs, apparently oblivious to her monstrous nature, talked her into taking him on as her agen
Big Mother is superhuman in strength, durability and stamina - she is a demon and thus is immune to ageing, disease or many forms of harm - she likely has sorcerous powers but has not shown any outright, she can take alternate forms but retains a lot of her demonic visage no matter what form she may take.
She is also a vicious predator who can devour people whole and has the standard predatory traits of extremely sharp claws and fangs - being a demon also means she is sadistic, intimidating and generally unpleasant to oppose as her very appearance and nature would cause fear and panic in those not used to combating such supernatural creatures.
Big Moher is a demon and thus has a sadistic personality, she is particularly fond of devouring humans alive, this sadism doesn't seem to spread to her own kind and she is a protective mother who cares for her young and will not hesitate to avenge them if they are harmed in any way - unsurprisingly this means she is particularly vengeful in regards to Beowulf, the man who nearly killed her son.
She also does not take kindly to others trying to use her for their own means and is thus driven primarily by her own desires, as is shown when she happily becomes a professional wrestler - simply because she enjoys the violence of the sport as well as the chance to eat her opponents alive (which many would assume was just part of her gimmick, unaware that she is very much serious in this threat).
- Big Mother has never revealed her true name and does so on purpose as knowledge of a demon's true name allows magic-users to hold power over them, this is also true in real-world demonology and occultism.