Mrs. Dennison appears to be a high-society London acquaintance of Fanny Dashwood’s, though they do not appear to be especially close. At one point, she hears that Elinor and Marianne are in town and invites them as Fanny’s guests to a party in her home, without knowing that the girls are not actually staying with the John Dashwoods.
As Fanny seems eager to attend this woman's party but not to make clear to her that the Dashwood girls are not staying with her, it's clear she seeks to impress Mrs. Dennison, suggesting she may be Fanny's social better.
