A lady is a woman who is the counterpart of a lord; or, the counterpart of a gentleman. "Lady" can be used as a title.
The primary meaning of "mistress of a household" is now mostly obsolete, save for the occasional use of old-fashioned phrases such as "lady of the house." This meaning is retained, however, in the title First Lady, used for the wife of an elected president or prime minister. In many cultures in Europe the equivalent term serves as a general title of address equivalent to the English "Mrs" (Gaelic Bean-uasal, French Madame, Spanish SeƱora, Italian Signora, German Frau)
The special use of the word as a title of the Virgin Mary, usually Our Lady, represents the Latin Domina Nostra. In Lady Day and Lady Chapel the word is properly a genitive, representing the hlaefdigan.
In the case of the younger sons of a duke or marquess, who by courtesy have "Lord" prefixed to their given and family name, the wife is known by the husband's given and family name with "Lady" prefixed, e.g. Lady John Smith; the daughters of dukes, marquesses and earls are by courtesy Ladies; here that title is prefixed to the given and family name of the lady, e.g. Lady Jane Smith, and this is preserved if the lady marries a commoner, e.g. Mr John and Lady Jane Smith.
"Lady" is also the customary title of the wife of a baronet or knight; the proper title, now only used in legal documents or on sepulchral monuments, is "Dame"; in the latter case the usage is to prefix "Dame" to the given name of the wife followed by the surname of the husband, thus Dame Jame Smith, but in the former, "Lady" with the surname of the husband only, Sir John and Lady Smith. During the 15th and 16th centuries princesses or daughters of the blood royal were usually known by their Christian names with "The Lady" prefixed, e.g. The Lady Elizabeth.
White's anecdote touches on a phenomenon that others have remarked on as well. In the late nineteenth and early twentieth century, in a difference reminiscent of Nancy Mitford's U vs. non-U distinction, lower class women strongly preferred to be called "ladies" while women from higher backgrounds were content to be identified as "women." Alfred Ayers remarked in 1881 that upper middle class female store clerks in his day were content to be "saleswomen," while lower class female store clerks, for whom their job represented a social advancement, indignantly insisted on being called "salesladies." Something of this sense may also be underneath Kipling's lines:
These social class issues, while no longer on the front burner in the twenty-first century, have imbued the formal use of "lady" with something of an odour of irony.
It remains in use colloquially; for example, as a counterpart to "gentleman," in the phrase "ladies and gentlemen," and is generally interchangeable (in a strictly informal sense) with "woman." (e.g., "The lady at the store said I could return this item in thirty days.")
Some advocates of non-sexist language recommend not using the word at all, whereas others permit its parallel use in the same circumstances in which a man would be called a gentleman or lord (for example, titling washrooms Men and Ladies would be considered sexist, but using either Men and Women or Ladies and Gentlemen would be acceptable; as is landlady as the parallel of landlord.)
In the United States, notably among younger feminists of the 1990s and 00s influenced by riot grrl, "lady" has occasionally been reclaimed in a more ironic fashion. For example, Miranda July's Joanie 4 Jackie chain letter videotape project is said to consist of "lady-made movies," a feminist music and video distributor in North Carolina called itself Mr. Lady Records, and chorus of Le Tigre's song "LT Tour Theme" from the album Feminist Sweepstakes (2000) declares itself to be written "for the ladies and the fags."
"Lady" is also the title of a 1980 chart topper by Kenny Rogers. It reached #1 in the US pop charts for 6 weeks and #12 in the UK. It was written by Rogers friend, Lionel Richie (who also did the song himself). The song appeared on Rogers' 1980 "Greatest Hits" album, which also reached Number 1 in the United States and sold over 30 million copies world-wide.