Isolate a honeybee from her sisters and she will soon die.
As you have no doubt realized, the quotes opening each chapter of this novel are both insight into some of the themes of the book (through bee symbolism) but also foreshadowing of events in the book. You can make your own prediction as to what such a quote might be foreshadowing.
As for thematic revelations, this quote speaks to more than one. First, a predominant theme of the book is female relationships, and the necessity of women to connect with other women for personal growth and a sense of identity. This quote speaks directly to this idea. The message here is that female relationships and a connection to a community (according to this quote) is not merely a suggestion for women to be happy, it is required for them to live.
Secondly, this quote speaks to the feminist ideals presented in the novel. This chapter includes a conversation between Lily and August, where August reveals why she never married:
There were enough restrictions in my life without someone expecting me to wait on him hand and foot. (145)
In all of her talks of love and relationships, August Boatwright is against the institution of marriage. She believes it would mean losing her sense of self, her true independence. This stems from a very feminist idea that in a male-dominated society, men hinder women from becoming who they are meant to be. Certainly this is one issue raised in the book that remains left open for personal reflection.