The cover says this book is a companion to Graceling, but you can read it without having read Graceling. From what I can tell, having not read Graceling, the two books take place in the same world but only very lightly touch on each other.
The titular character of Fire is a human monster, the last of them in the Dells. Monsters have the physical forms of normal animals, but have very unusual colors - there's a sky-blue rabbit monster mentioned in the book, for instance. Fire herself has amazingly red hair that resembles a fire.
Monsters crave human flesh and, especially, the flesh of other monsters. They stun people with their beauty, then get inside your head and make you passive while they kill you. From what we see with the human monsters, it's a form of psionics. Fire, and her father Cansrel, are both very powerful coercive psionics. They literally cannot turn off the basic effects shared by all monsters, but, being human, they can and have learned more things to do with their abilities than the animals monsters have. (I suspect the smarter animal monsters could also learn a few of the things Fire and Cansrel can do.)
There's this amazing running counterpoint in this book between Fire and Cansrel. The attraction the human monsters naturally generate has had vastly different effects on Fire than it has on her father. People react to a woman with those powers far differently than they do to a man.
I like how soft and relaxed the romance in this book is. It's not the focus of the plot. It's not even a focus of the subplot. It's just there, running under various other things. She falls in love with him, he falls in love with her, they don't make a big deal about it. There's more important things going on.
Specifically, they are trying to strengthen the position of the King of the Dells. Cansrel was the adviser of the previous king, and he pretty much dominated the man and drove the kingdom into the ground with his appetites and temper. So now Fire is struggling to use her powers for good, help the current king and prince deal with various uprisings, and live at court after a lifetime of living in isolation in the mountains.
Such an awesome book. Very enjoyable.