Mood is the emotional atmosphere of a book. It is created by an author's careful use of words, so it makes sense that it would be important in this book, where everyone in the community cares so much about precise language usage.
Jonas is very precise about language, like most members of his community. By choosing his words so, he is also carefully affecting the mood. Consider this example from the beginning of the book, when Jonas indoctrinates us into the rigid world of the community.
It was almost December, and Jonas was beginning to be frightened. No. Wrong word, Jonas thought. Frightened meant that deep, sickening feeling of something terrible about to happen. Frightened was the way he had felt a year ago when an unidentified aircraft had overflown the community twice. (Ch. 1)
The word “frightened” is rejected by Jonas, but it still affects the mood. It foreshadows trouble. Words like “sickening,” “made his stomach churn” and “urgent” convey a sense of danger in the community. Even though Jonas settles on “apprehensive,” which is a milder word, the fact that the Ceremony of Twelve is such a confusing and nerve-wracking concept creates a mood of suspense and curiosity for the reader.
There are other instances where a focus on language is also used to convey the mood.
"Do you love me?" There was an awkward silence for a moment. Then Father gave a little chuckle. "Jonas. You, of all people. Precision of language, please!" (Ch. 17)
Jonas is being precise. He is asking his parents if they care about him in the ways that people used to, in the days of the memories. They have no idea what he is talking about though. To them, love has no meaning.
This conversation comes as little surprise to Jonas, because has not not been raised with the concept of love. His parents have never shown him real affection. They are not his real parents. They are two random people who were matched for the capability of being able to get along, and then given two random children. He uses the word to see if they know what it means, and then they scold him for using a word that has no meaning.
This conversation does create a sympathetic mood here though, or perhaps frustrated. Jonas feels both for sure. He is somewhat angry and annoyed at his parents, and feels for what they have lost. He goes to see Gabriel and tells him about a world where there might be love, telling him, “things could change” (Ch. 17). Jonas wants to make his world a better place. He chose to use a word that his parents would find jarring in order to see how they would react.
The real lesson in this book is that people cannot give up their humanity in exchange for happiness. Happiness is an illusion. The emphasis on language precision is akin to our focus on political correctness today, taken to an extreme. We cannot be so obsessed with pleasantries that we forget how to feel, and how to live. Life is about emotions. Yes, that means sometimes there will be pain. You have to take the good with the bad. If giving up the bad means also giving up the good, it is not worth it.