Breaking from her narrative, Nelly tells Lockwood that these events transpired a little over a year ago. Lockwood is so enraptured with the story that he begs her to continue.
Cathy obeys her father's wishes. Nelly tells Edgar that Linton is of frail health, and Edgar admits that he fears for Cathy's happiness. He even concedes that if marrying Linton would make Cathy happy, he would be in favor of it, even though it means Heathcliff would get what he wants.
Although Linton never visits the Grange, after much pleading, Edgar allows Cathy to visit with Linton on the moors.
This short chapter is important for two significant reasons. First, it establishes the time frame, the previous winter, which is relatively close to Lockwood's arrival, and second, it establishes Edgar's mindset shortly before his death.
Because the current events just occurred the previous winter, the characters who Lockwood encounters at Wuthering Heights may still be closely affected by the events that have transpired. Recall that at Lockwood's visit to Wuthering Heights, Heathcliff had just recently lost his son and Cathy, her husband, and the way they reacted to the loss was indicative about their natures.
Edgar, now and up to the time of his death, remains misguided. He only wants Cathy's happiness, but happiness is something he was unable to provide for her mother, and it is something that he is unable to provide for their daughter.
avaricious greedy for riches.