The parents die.
There are two princesses. Elsa has ice powers she can't control, and almost killed her little sister Anna with them in the first five minutes. Elsa keeps her powers a secret from the world and lives in isolation and mortal terror of hurting someone. Anna had all her memories erased, and has no idea why Big Sis stopped playing with her, and the castle was locked up and most of the staff fired. Anna spends the ensuing years going slowly insane from loneliness and boredom. Their parents die and several years later Elsa is crowned Queen of Arrendale, opening the castle gates for the first time since they were very small, by which time the sisters are effectively strangers to each other.
Anna, being the cheerful impulsive one, meets a guy that morning and agrees to marry him that night. Elsa has a sensible reaction, which turns into an argument, which leads to Elsa revealing her magic to the world and fleeing Arrendale, freezing the city and harbor in the process. Anna pursues, meets an outcast ice-seller and his reindeer, and a living snowman Elsa unintentionally created while reveling in her powers and her ability to use them on a mountaintop with no one around to get hurt. She also makes an ice palace.
Hijinks of the wacky variety occur, Anna and sidekicks get to the ice palace. Unfortunately, Anna has not learned her lesson about backing off and giving her sister space while she's freaking out, and gets tagged with another ice-bolt. This leads to her heart slowing freezing, which will kill her unless some act of true love is performed on/by/with her. Her sidekicks and manly ice-seller rush her home to her new fiancé, but it turns out he was -gasp- only using her to get to the throne! And he's captured Elsa!
Further hijinks ensue, including the comedic sidekick snowman explaining what love is. Followed by the line "Bad news, I guess Christof doesn't love you enough to leave you." And this ends with Elsa creating a blizzard and all the main characters wandering around the frozen harbor in it: Elsa running, the villain pursuing, the lovebirds going for that lifesaving kiss. To stop Elsa, the villain tells her she killed Anna, which makes the blizzard stop. And Anna uses her body to shield her sister from the villain's sword, which is enough act of true love to save her after the fake-out. Yeah, the dying princess saves herself and the manly hero is sort of superfluous to the climax. I'm cool with that.
Which is where the pat ending comes in, once the snowman explains to Elsa and the really young or slow audience members why Anna isn't dead, she figures that all she has to do is focus on her feelings of love to unfreeze everything. Guy and girl get together, sisters resolve their differences, villains get their comeuppance, wacky hijinks with the minor characters, roll credits.
All the duets between the sisters really set up how different, yet alike they are. Elsa is calm, reserved, responsible and lives with a crushing terror of letting anyone close enough to harm, while Anna is a bubbly extrovert starved for human interaction. They both effectively grew up alone after the accident and their parents' deaths, and they react in different ways to that. Elsa is happy to be alone, she can't hurt anyone, Anna hates to be alone. It's very easy to empathize with both girls.
Actually, I really liked all the songs, even the snowman's intro song had enough clever word-play and sight gags to keep me entertained. And I'm pretty sure there was genuine Norwegian in the first song.
I won't give away the jokes, I'll just say there was only one gag in the thing that fell flat for me.
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