Lakoff's thesis is that metaphor is deeply embedded in the way we think about everything. So what happens when this mindset is turned to poetry, which is supposed to be metaphorical? Well, we get that it is even more metaphorical: it takes everyday metaphors, extends them in novel ways, and combines them into a dense interwoven structure that implies more than can the individual metaphors alone. It is the combination and overlapping of metaphors that gives poetry its added richness and depth. [Allegedly. I will admit right up front that I know nothing about poetry, and care somewhat less. But I am interested in Lakoff's ideas about cognition. And it seems worth studying those ideas where they occur in extreme situations -- like poetry.]
So Lakoff and Turner identify a bunch of metaphors used in everyday life (LIFE IS A JOURNEY gets a lot of mileage), and illustrate how they are used, extended and combined in certain poems. The point is that these metaphors are everyday concepts. They aren't just "pure poetry", in contrast to "literal" prose. Our understanding of how they work in the everyday context is necessary for our understanding of them in the poetical context.
Having dissected individual lines of various poems, the authors go on to analyse an entire (short) poem, "The Jasmine Lightness of the Moon", in terms of its layered metaphorical imagery. [If poetry had been analysed like this when I was at school, I might have been more interested. But then again, I'm interested in the analysis -- not the poem!]
But their key message is in the final chapter, on proverbs as poems, where they identify THE GREAT CHAIN OF BEING metaphor, deeply embedded in our culture and cognition, and deeply antithetical to ideas of equality and conservation.