Everyone fails at who they're supposed to be, Thor. The measure of a person, of a hero... is how well they succeed at being who they are.
~ Frigga to Thor.
Queen Frigga is a fictional protagonist in the Marvel Cinematic Universe, being a supporting character in the 2010 film Thor, its 2013 sequel Thor: The Dark World, and the 2019 film Avengers: Endgame.
She was the queen of Asgard and wife of its ruler Odin, mother of Thor and also the adoptive mother of Loki, who is also the son of the Frost Giant king Laufey. She was known for her supportive and comforting care, showing compassion towards Loki after his treachery, and for the mortal Jane Foster when Thor brought to Asgard. Frigga sacrificed herself to protect Foster from the Dark Elves causing Odin to mourn her death and declare war against Malekith. Thor would meet his mother again when he time-traveled to 2013 to collect an Infinity Stone, and would give him the confidence he needed to undo the decimation.
Frigga was born eons ago and was raised by witches during her youth, and they presumably taught her magic such as illusion casting and clairvoyance. She would later meet the Norse God Odin, and the two fell in love and married, becoming the benevolent ruler of Asgard. Though Frigga's relationship with her stepdaughter Hela isn't known, she would have a son named Thor with Odin, becoming the next-in-line to rule Asgard. When Odin defeated the Frost Giants in Jotunheim, he brought their king, Laufey's son Loki to the family, and Frigga treated both Thor and Loki equally. She later became aware of Loki's insecurities to his adoptive father and brother, and trained him in magic so that he wouldn't feel overshadowed.
When Frigga learned that Odin exiled Thor from Asgard for his arrogance and recklessness, she showed disgust and confronted her husband for his cruelty. After Odin went into odinsleep, she went onto care for him as Loki took the throne of Asgard, and later lied to Thor that their father had passed on. When Loki brought Laufey and the Frost Giants into Asgard, Frigga attempted to protect Odin until she was knocked aside by one of them. Though Loki managed to stop Laufey from killing Odin, Thor returned and revealed his deceptions to Frigga, and that he attempted to kill him and his allies on Earth. She then witnessed Thor and Loki battle on the rainbow bridge until Loki seemingly died from flying into a black hole, as Thor destroyed the bridge allowing Asgardian to travel to other realms. Afterward, Asgard celebrated Thor's return as he and Frigga mourned the "death" of Loki, and Sif comforts the queen of her loss.
Thor: The Dark World
Thor managed to capture Loki with the help of the Avengers on Earth, and the trickster god was imprisoned in Asgard for his crimes. Frigga attempts to comfort Loki and help redeem him, but he rebuffs her attempts and shows himself to be embittered towards Odin and Thor. When Thor brought Jane Foster to Asgard, Frigga gave her support and advice during her time there, and even protects her from Malekith and the Dark Elves. She was captured by Kurse and killed by him on the command of Malekith, as she had created an illusion of Foster with the Aether. Odin and Thor came to the room and mourned her death, and she given as a proper funeral where her spirit entered Valhalla. Though her death caused Odin to declare war against the Dark Elves, it allowed Loki to redeem himself to aid his allies in stopping Malekith.
Odin mentions Frigga when speaking to Thor and Loki before his death, telling them that he can Frigga calling him to come with her to Valhalla. Odin's death allowed his daughter Hela escape, and she attempted to overthrow Asgard and conqueror other realms after she was imprisoned. Thor, Loki and their allies succeeded in stopping Hela, but at the cost of the destruction of Asgard by the fire demon Surtur.
When the Avengers began their time heist to collect each Infinity Stone from different timelines, Thor and Rocket Raccoon are tasked with going to Asgard in 2013 to collect the reality stone. Frigga encounters Thor, and realizes that he is not of her child of the time, revealing to him that she was raised by witches. She gives him comfort and the confidence to accept failure and continue his mission, and Thor collects Mjølnir before returning to his time with Rocket.
She was originally more prominent in the first film, but most of her scenes were cut. Kenneth Branagh wrote her a "nice note" in response and apologized for this, and the actress happily returned for the sequel.