Carla Yeager is a looper in the highly damaged Attack on Titan Loop.
Carla is a tallish woman with long black hair and amber eyes. She is often described as resembling her son, Eren. In loop, she is typically found wearing simple civilian clothes.
Carla married Grisha Yeager, gave birth to Eren, raised him, took in Mikasa Ackerman when she was orphaned, raised her, was a good mother, and soon after Wall Maria fell, she was crushed under a boulder, told her children to leave her to die, cried, and was eaten by the Smiling Titan. She died.
She really didn't do much beyond be a good mom and die to kick off the plot. Course, her constant dying was also one of the mainstays of the loop: no matter how hard Eren worked or how much medical knowledge he accumulated, she'd never recover from being crushed. As such, she never survives when she isn't awake, or when she lacks her liquefaction powers.
Late into the loops (around the same time Hurricane Billy was blowing about), Carla was forcibly activated by Ganesha in an attempt to bulwark Eren, Mikasa and Armin's degrading sanity. As was custom by then, Carla's first loop was a fused loop, one into Fullmetal Alchemist. Here, she assumed the role of Edward and Alphonse Elric's mother Trisha, and later the homunculus Sloth. Due to the traumatic nature of being a homunculus though, Carla's own sanity nearly shattered, as she was caught between her memories, Trisha's memories, and Sloth's programmed hatred of humans. In a supreme act of will, bolstered by her knowledge of Dante's plan for her and her memories of Eren and Mikasa, Carla restored her persona and turned against Dante, being instrumental to her defeat. Soon after, the loop returned her to the Walled World, and Carla was joyously reunited with her beloved children.
Liquefaction: She possesses the ability to liquefy portions or her whole body, granting her exceptional immunity to physical attacks, as well as innate skills in espionage and spy craft.
Evangelion Pilot Skills: Does not possess a personal Evangelion, but is skilled with piloting it.
Subspace Pocket: Like all loopers, is capable of creating a small pocket where she can store things between loops.
Eren Yaeger (Attack On Titan): Her son. She was a good mother, he was a cheeky son, and they both love each other very much.
Grisha Yeager: Her husband. Despite turning their son into a weapon, she does love him very much.
Mikasa Ackerman (Attack on Titan): Her adoptive daughter. The relationship is... loose, but since Mikasa has fond memories of the woman that took her in, and Carla did her best to raise her foster child, there is genuine affection between them.
Hannes (Attack on Titan): The only other looper she knew from baseline, Carla has occasionally turned to the elder looper for help and advice.
Levi Ackerman (Attack on Titan): Levi's opinion of Carla is as such: All Jaeger's are too damn stubborn.