Alice finds herself in the beginning of this chapter in the annoying company of the Duchess. They conversed, sort of, about the goings on of the day, but mostly Alice thought to herself and the Duchess tried to find simplistic morals in everything. The conversation, on the whole, ended up being about how boring politeness can be at times, and how too much politeness can threaten the mind. The conversation is ended, however, by the Queen, who brings Alice back into the game. The game moves forward, interestingly, out of a fear of the Queen rather than out of any fun the game might have produced. Once all of the other players have been sentenced to death and the only people not in the custody of the soldiers are Alice and the King and the Queen, then the Queen tells Alice she must hear the Mock Turtle's history.
(While the Queen was distracted, the King pardoned everyone).
The Queen has a Gryphon take Alice to the Mock Turtle.
The Mock Turtle was crying when they approached him. Slowly he tells them about his schooling, which was in the sea. Mostly, the story sets up the next chapter, where Mock Turtle is to tell Alice about the games they played.
This chapter is a bit of a transition from the Croquet game to the Mock Turtle's Story and it is hard to say what else is in it. There is a good deal of wordplay between Alice and the Duchess at the beginning, but other than that it only prepares the reader for the next chapter.