Life becomes a social whirlwind for the Dashwoods, mostly due to the many gatherings put together by Sir John. The month of October is spent with parties, dances and outings. As Sir John always invites Willoughby as well, Willoughby and Marianne spend much time together publicly.
Noteworthy in this chapter is the developing friendship between Elinor and Colonel Brandon. Just last chapter, Elinor noticed that Mrs. Jennings appeared to have been right, and that Brandon indeed had developed a bit of a tendre for her sister. In this chapter, Brandon tips Elinor (and us) off to this when he quizzes her on Marianne's position on second relationships.
Marianne believes that everyone gets one true love in life. A second attachment is therefore out of the question, as far as she is concerned, and one can imagine that between Marianne's habit of expressing her true opinion on things pretty much regardless of company and Mrs. Jennings's habit of chattering on about things, it's not strange that Colonel Brandon has caught wind of her belief.
That he enquires about Marianne's beliefs and opinions is tantamount to an admission that he is interested in her. That he is working so hard to figure out exactly what her opinion is shows that he is likely very interested in knowing and understanding her.
It is also an admission that he himself had a prior attachment, even though he is known to be a bachelor. His further comments about knowing a certain lady offers further support for his having had a prior relationship, and with his having been disappointed in love.
You'll note that Elinor thinks Marianne will benefit from a few years out in society, and this reminds me of something I probably ought to mention. Since Marianne is only 16-1/2 at the start of the book (and is probably 17 by this point in time), she really hasn't mixed in society all that much. She is likely to have been "out" in society only since she turned 16, and a good 6 months of her time being "out" in society was spent with family at Norland, in deep mourning for her father. So Marianne really is as young, inexperienced and idealistic as Elinor and Brandon give her credit for being.
But where Elinor wishes for Marianne to have "a better acquaintance with the world", Brandon disagrees, saying that sometimes the world proves too cruel for young people with Marianne's romantic sensibilities.