To understand the meanings of each quote about bees in the beginning of each chapter of Sue Monk Kidd's novel The Secret Life of Bees, you first want to understand the fact being explained in the quote and then connect the fact to key events or themes in the chapter that follows.
The first quote explains the fact that the queen bee holds the community of the beehive together. She is the leader of the other bees, and if she is no longer in the hive, the other bees feel lost. As the quote states, "The workers very quickly sense her absence." The passage continues to state, "After a few hours, or even less, they show unmistakable signs of queenlessness." In other words, the whole hive falls into a state of panic, distress, and chaos. But a fascinating theme in this quote is the queen bee leaving the hive. To further understand the quote and how it relates to the following chapter, or even the novel as a whole, one may need to look up various reasons why a queen might leave the hive.
There are really only a few reasons why a queen will leave the hive. The first reason is for what is called "her maiden flight" in which she is fertilized by drones. A second reason is if the hive becomes overcrowded; once scouts pick out a location for a new hive, she'll then lead the swarm to the new hive. The third reason is the most dramatic and most important reason--she has died. And, as we can see from the rest of the book, death is a major theme.
It's also important to think about what author Kidd is using the queen bee to symbolize. We know that the queen gives birth to all the worker bees, so she is quite literally the mother of the hive. As we continue to read the first chapter, we learn that the protagonist Lily Owens has become obsessed with death since she was told by her father that she accidentally shot and killed her mother. Since her mother is dead, Lily is quite literally without a queen bee in her life. Lily's caretaker Rosaleen, which interestingly rhymes with queen, has taken on the role of queen bee in Lily's life, but Rosaleen proves to be an unstable queen when she is persecuted by racism and arrested for assault.
In the chapter, we see just how much Lily is missing her queen bee, her mother, in her life when she describes her hallucinations about swarms of bees, which Rosaleen said was an omen of death, and when she describes her fantasies about being with her "mother in paradise." She describes that she pictured her mother, for the "first ten thousand years," "kiss [her] skin till it grew chapped and tell [her that she] was not to blame" (p. 3).
Hence, we see that the quote is meant to symbolize the absence of Lily's mother and capture the theme of death.