In this chapter the Turtle describes a kind of line dance (a quadrille) which is acted out between many assorted sea creatures each paired with a lobster for a partner. However, the principle part of this chapter is actually devoted to the Song sung during the quadrille.
After singing the song of the Lobster-Quadrille, the Mock Turtle and the Gryphon speak with Alice. Finally the conversation comes around to Alice and she tells them her journeys up to that point. The story is stopped when Alice gets to the part about her misremembering "Old Father William." The Turtle asks her to try and repeat something else so he can see if everything is coming out wrong. They ask her to repeat a rhyme called "'Tis the voice of the sluggard."
It all comes out wrong, so the Mock Turtle demands that it be explained. But Alice has no clue what it all means when it comes out so strangely. So, Alice finally stops her reciting and asks the Turtle to sing her a song, which he does. He sings "Turtle Soup."
The chapter is finally cut short, part way through the Turtle's song, by an announcement. In the distance someone calls out "The trial is beginning!"
Even without the Mock Turtle crying all of the time (which he does) this would still be a very sad chapter. Basically this chapter is concerned with what has been lost. It's about the past, and about memory. The Mock Turtle seems to be equating his student days, his childhood, with the time when he was a Real Turtle. Now, as an adult, he doesn't feel as though he is alive or real anymore. The chapter ends with that very gruesome song about Turtle Soup. It is very strange because up to this point the great taboo of Wonderland for Alice is the discussion of eating animals because all of the animals don't want to face their own mortality. Now, however, it seems that the Mock Turtle feels an overpowering sense of nostalgia for his childhood and therefore is a bit obsessed with death as his only alternative. It seems to him that nothing makes much sense anymore, now that he is out of school. The fact that Alice can't seem to even remember her school lessons properly makes matters more pointed for the Turtle, making him feel even more alone perhaps.