I have edited your question a bit because you have asked two questions. If you want an explanation of a particular epigraph beyond the one I use as an example, you will need to ask another question. :)
The epigraphs about bees relate to Lily because humans and bees are social beings. In particular, bees cannot exist without their queen, and Lily, because she has grown up without a mother, needs a "queen bee," too.
The epigraph for the first chapter is as follows:
The queen bee, for her part, is the unifying force of the community; if she is removed from the hive, the workers very quickly sense her absence. After a few hours or even less, they show unmistakable signs of queenlessness (1).
Even without knowing anything about the story, a reader can tell that the queen bee is important and that somehow, there will be a queen bee in the story. As we read the chapter, we see how Kidd has tied all of this together, with the bees that appear to Lily and with the understanding that she has lost her queen bee, her mother.
In each chapter, the epigraph gives us a key to what is important in the chapter, what bees and people have in common.