King Agnarr and Queen Iduna were the rulers of Arendelle. Together, they had two fair daughters, Elsa and Anna. Although Anna was a normal child (like her parents), Elsa was born with powers of ice and snow. Apparently, the parents are as powerless as Anna, but it can be presumed that either magical abilities run in the family and merely skipped their generation, or that Elsa was randomly born with magic for whatever reason.
Judging by how he presents himself, Agnarr is learned, kind, powerful, and diligent. Iduna appears to be far more passive, gentle, and openly emotional than her husband, though with the crucial motherly nature needed to raise Anna and Elsa. Their personalities are further explored in the novel A Frozen Heart, where several traits are revealed, including the fact that Agnarr has the tendency to spoil his daughters, and has a difficult time legitimately punishing them when they misbehave. Whenever he loses his temper, Iduna was able to calm his nerves. This peacekeeping aura of the queen is also carried over to other occasions, such as Elsa's training to control her powers; the queen was an advocate for momentary breaks, in hopes of preventing Elsa from becoming overwhelmed.
With that, it was clear that the rulers' primary concern lie within their daughters, willing to make large sacrifices to ensure their safety due to Elsa's unique abilities, and despite Elsa's powers, they don't fear her in the least, giving her just as much affection as Anna, and are even willing to make physical contact with her, but eventually decided against doing so, as Elsa prefers it that way, fearful that she might hurt them.
In spite of Elsa's crippling fear of harming her parents, neither Agnarr or Iduna have ever shown fear of their daughter—only sympathy, and the fear of the hardships that may befall her should her abilities remain untamed. In fact, they appeared rather optimistic that she would one day learn to control her abilities with ease, with Agnarr noting the drastic isolation was meant to last for a temporary amount of time, until she learns to control her powers. By the time of their two-week voyage, they were so confident in their eldest daughter, that they had even planned to end the isolation, once they returned.
Their names are not in the film's credits, but are seen written in the Runic alphabet on their memorial stone markers. According to those, the name of the king is Agðar (English: Agdar/Agnarr) and the name of the queen is Iðunn (English: Idun/Iduna). However, this has not been confirmed by the filmmakers.
- The Queen's Name: Iðunn can be anglicized as Ithunn, or Idunn/Idun. Iðunn means 'youthful', 'eternal youth' 'again to love'. The name Idun is a popular name in Scandinavia, the setting of Frozen. The name Idun also means 'rejuvenation'.
- The King's Name: Agðar can be anglicized as Agdar. Agðar is a male form of Agða, a short form of Agatha, meaning 'good, honorable.' Agdar is a popular name in Norway. The name Agdar means 'brave warrior' in Norse and from Greek agathos, meaning 'good'.
- Due to the Runic alphabet, the king's name can also be read as Akðar or Akthar. Some believe it could be the name Akhtar, which means 'star' and 'good luck'. The latter name is found in India, Pakistan, and Bangladesh as well as Iran as a surname thus making it unlikely to be the given name of a Nordic King.
In the middle of the night, Elsa and Anna, against rules, sneak into the Grand Hall to create a winter wonderland for their enjoyment. During their playtime, Elsa accidentally strikes Anna in the head with her powers, rendering the latter unconscious. Agnarr and Iduna quickly arrive onto the scene upon hearing the distressed calls of Elsa, and Agnarr quickly thinks of a possible solution, and uncovers a map leading to a valley inhabited by magical, healing trolls.
Agnarr and Iduna bring Elsa and the unconscious Anna to the valley, where the king of the trolls, Grand Pabbie, informs them that Anna can be healed, though they are lucky she was not hit in the heart, for it can be fatal. To restore Anna's health, Pabbie cleanses her body and mind by removing all elements of magic, including memories of magic, meaning Anna will have no memory of Elsa's powers once she awakens. Pabbie then informs the royal family that, while Elsa's magic is beautiful, she must learn to control it and not let fear consume her; should she do otherwise, horrible events may occur. Agnarr nevertheless assures his wife that Anna will be protected, and Elsa will eventually learn to control her abilities.
Having taken Pabbie's saying of "fear will be your enemy" literally, Agnarr and Iduna make the decision to limit Elsa's contact with others by separating her and Anna and keeping fewer people in the castle by locking the castle gates and reducing the staff until Elsa garners complete control of her powers. They move Elsa and her belongings into a separate room. As the years pass, and Elsa grows, Agnarr and Iduna are Elsa's only true form of human contact. They work with her on concealing her powers by concealing her emotions. To further help, Agnarr advises Elsa to wear gloves, and coins the mantra, "Conceal it, don't feel it, don't let it show", which Elsa would carry onto adulthood.
One day, Agnarr and Iduna are to set off on a two-week sea voyage. During a storm, they are drowned at sea by monstrous waves. Anna and all the people of Arendelle mourn their deaths (a portrait of the couple is draped over with a black sheet of fabric), but Elsa doesn't attend the funeral out of fear of her powers being revealed and someone getting hurt as a result. Due to the untimely tragedy, Elsa's training was left incomplete, her powers still mostly out of her control.
Although Iduna isn't seen after their painting is drifted by the curtain, Agnarr still appears later in the film; in a painting of his own coronation seen hanging in the library of the castle when Elsa was trying to control her powers, and again when Prince Hans betrays Anna in order to take over the kingdom. They are both mentioned when Kristoff asks Anna during their argument over Anna getting engaged to Hans after just meeting him, "Didn't your parents ever warn you about strangers?" to which Anna replies (rather uncomfortably), "Yes, they did." while slowly moving away from him.
Agnarr and Iduna briefly appear in Elsa's flashback during the reprise of "Ring in the Season". When Anna asks Elsa if their family has any holiday traditions, the only instance that Elsa could recall was the annual ringing of the Yule bell, although Anna pointed out that the Yule bell ceremony was more for the kingdom, rather than something personal to their family.
Anna and Elsa's parents appear in live-action form in the first episode of the fourth season, which has the backstory of the events happening in Arendelle prior to Frozen. Although Anna and Elsa's mother was identified as Iduna based on translation of the Runic inscriptions on her tombstone in Frozen, here, she is called Gerda (a character named "Gerda" does appear in Frozen, but she is one of the servants, not Elsa and Anna's mother). She is portrayed by Pascale Hutton as an adult and by Ava Marie Telek as a child.
Ingrid fears hurting her sisters with her powers, but her sisters promise to help conceal the powers, and continue to sustain their unity. Years later, on the night of their father's birthday celebration, Gerda and Helga attempt to convince Ingrid into coming with them, but her fear of ruining the party overshadows her sisters' pleads. At the party, Helga introduces a new admirer, the Duke of Weselton, to their father.
After the party, the sisters arrive home to find Ingrid packing up as she believes with herself gone, they can have normal lives, fearing she won't be able to control her powers. Gerda mentions Rumplestiltskin, who may help. In exchange for their ribbons (which the sisters used to symbolize their sisterhood), Rumplestiltskin gives Ingrid a pair of gloves to conceal her powers, as well as an urn to entrap her if she becomes too dangerous. Later, in the royal garden, Gerda comes across Ingrid crying over the frozen and crumbled body of Helga. Realizing Ingrid, whether intentionally or not, killed Helga, Gerda entraps her in the urn. She then seeks out Grand Pabbie and asks him to erase her sisters' existences from everyone's memories, even though he implies a magical price will be extracted at her expense.
After marrying her husband, they rule as Queen and King of Arendelle and give birth to Elsa and Anna. When Elsa exhibits powerful and dangerous ice powers, the couple travel to the nearby land of Misthaven to find a wizard to get rid of her magic. On the return trip home, the ship is caught in a maelstrom. Realizing they might not make it out alive, Gerda hastily writes a note, places it into a bottle and throws it overboard in the hopes Elsa and Anna will find it. Soon after, the ship capsizes and sinks, drowning them.
Gerda's message winds up on the beach of Storybrooke 35 years later. A recently thawed out Anna finds the note and brings it to the Snow Queen's cave. There she reads it to Ingrid, Emma, and Elsa. It explains that the couple was wrong to keep the two girls apart and to hide Elsa from the world. Gerda also explains that she feels guilty about what she did to Ingrid and wishes that she could take what she did back.
- Many fans have noted that Agnarr bears a striking resemblance to Walt Disney in his younger years.
- In the Frozen book illustrations, Agnarr has dark hair and Iduna has light hair, but in the movie, it's vice-versa.
- Iduna's character model, upon closer look, is simply a recolored and customized version of Elsa's coronation appearance, such as her wearing her hair in a crown-twist bun (only with brunette hair instead of platinum blonde). There have been several differences, including her clothing and dark brown hair, and her face is thinner than both of her daughters, but her face and eyes resemble both girls.
- The ship that Agnarr and Iduna were on resembles the ship Ariel and Flounder found and explored in their introductory scene in The Little Mermaid.
- In Once Upon a Time, Iduna's name is Gerda, which was the original name of the heroine in the original "Snow Queen" fairy tale, who was the inspiration for her daughter Anna.
- According to the book A Frozen Heart, Iduna has a sweet tooth.
- According to the read-a-long book "Anna and Elsa's Winter End Festival", the queen had quite a sweet tooth, and believed in fresh air and exercise. Her birthday is said to be "at the end of winter, right before spring."
- After her death, Iduna's belongings were stored within the castle passageways.
- In Frozen: Live at the Hyperion, Agnarr and Iduna briefly return as spirits watching over their reunited daughters, during the finale.
- In the film, the only thing Iduna says is "She's ice cold."
- Iduna's sole line was recorded by Jennifer Lee, the films co-director and screenwriter. Coincidentally, Lee's daughter, Agatha, voiced 9-year old Anna.