Having to transition from Norland Park to Barton Cottage is a huge shock and a huge transition for the Dashwoods. Their manner at Norland was so grand and beautiful as to "engage the general good opinion of their surrounding acquaintance" (Ch. 1). However, the estate was left to Mr. Henry Dashwood's son, with nothing for his wife and daughters, except five hundred pounds a year. Therefore, upon Henry Dashwood's death, the girls are forced to leave Norland and accept a cottage to rent from another family member.
The cottage is certainly small in comparison to Norland manner, with only two sitting rooms, four bedrooms, and two garrets. It is comfortable and well built; however, the girls were disappointing because it looks nothing like what a cottage should look like. As Austen describes:
The building was regular, the roof was tiled, the window shutters were not painted green, nor were the walls covered in honeysuckles. (Ch. 6)
The mere size of the house and the fact that they no longer live in Norland is enough to bring tears to their eyes, but they are determined to be happy. Hence, one way that their arrival at Barton Cottage influences their lives is that they must learn to accept a significant change. They are now poor when before they were very rich.
In addition, their arrival at Barton Cottage helps move the plot forward because it is here that they meet some other central characters, especially Colonel Brandon and Willoughby, but also other characters like Mrs. Jennings, Sir John Middleton, and Lucy Steele.