The Honorable Miss Fisher

Because she is the daughter of a baronet. "The Honourable" title denotes that she is an aristocrat but holds no actual title of her own.

It's a title...we still use it today for people like politicians. I quoted the UK bit, though, because that's the context in which Phryne uses it.

https://en.wikipedia.org/wiki/The_Honourable

In the United Kingdom, all sons and daughters of viscounts and barons (including the holders of life peerages, but not judicial "Lords" who are not peers) and the younger sons of earls are styled with this prefix. (The daughters and younger sons of dukes and marquesses and the daughters of earls have the higher style of Lord or Lady before their first names, and the eldest sons of dukes, marquesses and earls are known by one of their father's or mother's subsidiary titles). The style is only a courtesy, however, and on legal documents they may be described as, for instance, John Smith, Esq., commonly called The Honourable John Smith. As the wives of sons of peers share the styles of their husbands, the wives of the sons of viscounts and barons and the younger sons of earls are styled, for example, The Hon. Mrs John Smith. Likewise, the married daughters of viscounts and barons, whose husbands hold no higher title or dignity, are styled, for example, The Hon. Mrs Smith.