I believe the author, Sue Monk Kidd, opens chapter 9 with the quote because of its reference to the need for communication. The quote tells of the importance of communication in regards to a honey bee and its society. In the case of Lily Owens, she has been carrying her secret inside her for awhile. She is living in the Boatwright's honey house and sleeping on their cot, but she has not given them a clue as to who she really is.
June, one of the sisters, has been reluctant to have Lily at the house but in the chapter she experiences a breakthrough with Lily after they have a water fight to cool off and fight over the hose. Lily fially gets the courgae to communicate the big question she needs answers to. "Did you know her mother?"
Lily learns that her mother stayed in the same honey house she is staying. his chapter begins to open the path of communication from Lily about the real reason she is with the Boatwrights.