It's a show of two halves. Some people love the whole thing and say it's a top anime comedy. Personally, I found the first half a bit dull and I don't think I laughed once during the first six episodes... but after that the show gets bored of its original formula and becomes a lot more varied and funny.
The premise is that the Demon King has kidnapped Princess Aurora and has her in his demon castle as a hostage. Beware, humans! I have your princess! Obey, or she will die! Unfortunately (for him), the princess is a sociopathic little idiot while all the demons are soft-hearted and pushovers. Hostages have nothing to do, so the princess just wants to sleep. She needs a good pillow. And a blanket. And a better bed. And anything else that crosses her tiny, tiny mind. She also doesn't really understand that people are people, not raw materials. Giant turtle? Blow it up for its shell. Sheet Ghosts? Cut it up for bedding.
In any normal show, she'd be evil. These demons, though, have unlimited resurrection magic, so it's all just slapstick. Besides, she's just as liable to kill herself in her misadventures, annoying her captors as they tell her to take more care of herself. This is a girl whose reaction to a giant poison mushroom is to go to sleep on it.
For me, this formula was fairly dull. 1. Princess behaves outrageously. 2. Demons passively react. And that's it. There are no consequences to anything and no one has even the faintest glimmer of intelligence. They're all idiots. The demons keep leaving super-powerful magical weapons lying around and then being surprised when the princess does horrible things to/with them. I was also mildly repelled by the princess as a person, although in fairness she's far too much of an airheaded space case to be called malicious. I don't think she really understands right and wrong. (It makes quite a lot of sense that a pampered royal would grow up with her view of the world, while furthermore she has some odd and slightly pathetic beliefs that her upbringing drilled into her. Very occasionally, you'll feel sorry for her.) Anyway, she's amusing and her exploits are colourful. She also has comedy eyes and an entertaining opening credits sequence.
Eventually, though, the show graduates from "princess does what she wants with no meaningful opposition". In ep.7, the demon king's would-be usurper brother kidnaps her. That was funny. For once, she's up against someone with (some) backbone and a (not very serious) dramatic motivation. Theoretically, she's in danger, with the resurrection spells all being in the demon king's castle.
Ep.8 shows us the princess's nightmares and childhood memories. (She was dozily evil then too.) The dentist is funny. The demons become as important to the show as the princess, who becomes arguably more of a comedy foil than a protagonist. They get "quests" of their own. (The princess's little jaunts of theft, vandalism, etc. had always been presented as "quests".) They try to raise the princess's awareness of her position as a hostage, give her work to keep her busy and let themselves get talked into accompanying her on a day trip to the human realm. They're soft-hearted, likeable goofballs (much nicer than the princess) and by the end they've become indistinguishable from surrogate parents.
There's an oddity in the princess's age, incidentally. She's tiny and looks like a child, but she has an adult fiance who looks the same age as her in childhood flashbacks. Well, never mind. The show's a silly comedy fantasy and there are any number of fan theories available for that.
I liked the show's second half and I particularly liked the last episode. She persuades the demons to let her pop home briefly, in the human realm. We learn that the princess reacts amusingly to hearing childhood stories told about herself and that she's been thinking about this whole Human-Demon Relationship thing. (Also, that her mother's a moron too.) That said, though, I won't be keeping the series. There's a lot to like about it, but its first half is fairly empty and kept sending me to sleep.