In the book, "precision of language" means using the correct words to convey the exact thought the speaker intends to communicate. In other words, by using precise language, the speaker can communicate the actual thought and not something that is close to the thought. The narrator even notes that:
the reason for precision of language was to ensure that unintentional lies were never uttered.
In the society of The Giver where everything is planned, precise language is expected from all citizens to avoid unintentional mistakes or accidents in speech. In fact, mistakes in general are not tolerated, including sloppy speech. The author provides a good example when Jonas says something that is not precise.
One day in school, Jonas exaggerates. Just before the class lunch break, he says that he is "starving.” Immediately, he is taken aside and chided for this statement or “lie.” He is told that since he was not actually starving, but merely “hungry,” he was speaking a lie. Even though the lie was unintentional, it is still not acceptable.
Viewing this rule through the lens of our more tolerant society, the reaction to Jonas' statement appears to be too harsh. It seems clear that most people would understand that Jonas was not really starving. His use of the word was intended to convey that he was very hungry and was anxious for the lunch break so that he could eat. However, in Jonas’ dystopian planned society, there is no allowance for exaggeration or what the society deems imprecise speech.