"Because the root of sanity is in the balls." (239)
What Oliver means in the above quote from chapter fifteen of Lady Chatterley's is that what makes people human is in the genitals, and without their humanity, their "spunk," they become empty shells without grounded rationality. They become insane, offering up each other to survive a little longer in the money machine of industry. This makes sense in a lot of ways. The genitals represent an instinctual part of the psyche; consciously or unconsciously, they can also be a core--something reliable. Our genitals are the anchors of our physical selves.
Oliver places a lot of faith in the "human reality" of genitalia and the myriad bodily functions they entail: "I don't want a woman as couldna shit nor piss" (245). Connie is a "real" woman because she inhabits her physical self, her body, her genitals. Obviously all living women expel bodily waste, but Connie isn't shy about her body. She and Oliver spend a lot of time naked in this chapter, in blatant acknowledgement of their flesh.
In fact, they're so excited about their nakedness that they decide to run around nude in the thunderstorm that's raging outside. Between the chill rain and the heat from their bodies, "the rain streamed on them till they smoked" (243). They have sex naked in the middle of the woods, then run back into the cottage to bask in the realness of their bodies.
It's all very pagan (here meaning pre-modern, Grecian, etc), this naked romping and this adoration of the body, when the society all around them promotes the mental, industrial, inorganic life. This imagery persists as Oliver goes outside and comes back with flowers:
"He had brought columbines and campions, and new-mown hay, and oak-tufts and honeysuckle in a small bud. He fastened fluffy young oak-sprays round her breasts, sticking in tufts of bluebells and campion: and in her navel he poised a pink campion flower, and in her maiden-hair were forget-me-nots and woodruff. [...] And he stuck flowers in the hair of his own body, and wound a bit of creeping-jenny round his penis, and stuck a single bell of a hyacinth in his navel" (250).He's adorning their bodies for the "wedding" of John Thomas and Lady Jane (their genitals, respectively). In many pre-modern traditions, many kinds of plants and flowers were used in such ceremonies, both as decoration and occasionally because of the plant's perceived special or magical properties. There are countless Greek deities, for example, who are depicted with plant adornments, with Dionysus being perhaps one of the most recognizable. He is often shown wound with ivy and holds a thrysus, which is a stalk of fennel or vine.
There are many other examples of flowers in any mythology, and I'm sure you know just as many as I do, so you get the idea. By draping themselves in plants and flowers, Oliver and Connie are harking back to a different time; they are removed from the modern, mental society and embracing the physicality of older traditions.