Most of this chapter is a digression that allows Dostoevsky to examine some of the prominent advanced ideas of the time — ideas that were influencing such people as Raskolnikov and to a much lesser degree, the simplistic Lebezyatnikov, whom Dostoevsky depicts as an advanced liberal and a comic rube. Basically, these discussions show Dostoevsky's extreme dislike and distrust for the radical young men who are too influenced by new ideas. The foolishness of Lebezyatnikov is supposedly the foolishness of any person who adheres so closely to the "advanced ideas."
Regarding the development of the plot, this chapter merely sets up the proper machinery for Luzhin's attempt to frame Sonya.
