The word lady is a civil term of respect for a woman among English speakers. It is the equivalent of gentleman. It is also a formal title in England. "Lady" is used before the surname of a woman with a title of nobility or honorary title suo jure, or the wife of a lord, a baronet, and a knight, and also before the first name of the daughter of a Duke, Marquess, or Earl throughout the United Kingdom. Once used to describe only women of a high social class, race, community, and status in Europe; now the term is commonly used to refer to any adult woman among English-speakers globally. Use of this word is still controversial, as is the term "gentleman".
The word comes from Old English hlǣfdige; the first part of the word is a mutated form of hlāf, "loaf, bread", also seen in the corresponding hlāford, "lord". The second part is usually taken to be from the root dig-, "to knead", seen also in dough; the sense development from bread-kneader, or bread-maker, or bread-shaper, to the ordinary meaning, though not clearly to be traced historically, may be illustrated by that of "lord".
The primary meaning of "mistress of a household" is now mostly obsolete, save for the term landlady and in set phrases such as "the lady of the house." This meaning is retained in the southern states of the USA, and also, in the title First Lady for the wife of an elected official. In many European languages the equivalent term serves as a general form of address equivalent to the English Mrs (French Madame, Spanish Señora, Italian Signora, German Frau, Polish Pani, etc.). In those languages it is correct to address a woman whose name is unknown as Madame, Señora, etc., but in polite English usage "lady" has for centuries only normally been a "term of address" in the plural, which is also the case for "gentleman". The singular vocative use was once common but has become mostly confined to poetry. In some dialects it may still be used to address an unknown woman in a brusque manner, often in an imperative or interrogatory context, analogous to "mister" for an unknown male: e.g., "Hey, lady, you aren't allowed in here!" In this usage, the word "lady" is very seldom capitalized when written. The usual English term for politely addressing a woman is Madam or Ma'am.
In British English, "lady" is often, but not always, simply a courteous synonym for "woman". It has a formal and respectful quality, being used to describe a woman in old age such as "an old lady" or when speaking about a woman to a child (e.g. "Give the money to the lady.") It may be used, however incongruously, in descriptions such as "the cleaning lady" or even "a bag lady" (tramp). Public toilets are often distinguished by signs showing simply "Ladies" or "Gentlemen".
In more recent years, use of the word is even more complicated. Alfred Ayer remarked in 1881 that upper middle class female store clerks were content to be "saleswomen", while lower class female store clerks, for whom their job represented a social advancement, insisted on being called "salesladies". The American journalist William Allen White noted one of the difficulties in his 1946 autobiography. He relates that a woman who had paid a fine for prostitution came to his newspaper to protest, not that the fact of her conviction was reported, but that the newspaper had referred to her as a "woman" rather than a "lady". After the incident, White assured his readers, his papers referred to human females as "women", with the exception of police court characters, who were all "ladies".
White's anecdote touches on a phenomenon that others have remarked on as well. In the late 19th and early twentieth century, in a difference reflected in the British historian Nancy Mitford's 1954 essay "U vs. non-U" , lower class women strongly preferred to be called "ladies" while women from higher social backgrounds were content to be identified as "women". These social class issues, while no longer as prominent in this century, have imbued the formal use of "lady" with something of irony (e.g.: "my cleaning lady", or "ladies of the night" for prostitutes). Commenting on the word in 1953, C.S. Lewis wrote that "the guard at Holloway said it was a ladies' prison!"
It remains in use, for example, as a counterpart to "gentleman", in the phrase "ladies and gentlemen", and is generally interchangeable (in a strictly informal sense) with "woman" (as in, "The lady at the store said I could return this item within thirty days."). However, some women, since the rise of second wave feminism, have objected to the term used in contexts such as the last example, arguing that the term sounds patronising and outdated when used in this way; a man in the same context would not necessarily be referred to as a "gentleman". One feminist writer, Robin Lakoff, in her book Language and Woman's Place (1975), notably raised the issue of the ways in which "lady" is not used as the counterpart of "gentleman". It is suggested by academic Elizabeth Reid Boyd that feminist usage of the word lady has been reclaimed in the 21st century. 
Formally, "Lady" is the female counterpart to higher ranks in society, from gentlemen, through knights, to lords, and so on. During the Middle Ages, princesses or daughters of the blood royal were usually known by their first names with "Lady" prefixed, e.g. Lady Elizabeth; since Old English and Middle English did not have a female equivalent to princes or earls or other royals or nobles, aside from the queen, women of royal and noble status simply carried the title of "Lady".
As a title of nobility, the uses of "lady" in Britain are parallel to those of "lord". It is thus a less formal alternative to the full title giving the specific rank, of marchioness, countess, viscountess or baroness, whether as the title of the husband's rank by right or courtesy, or as the lady's title in her own right. A peeress's title is used with the definite article: Lord Morris's wife is "Lady Morris". A widow's title derived from her husband becomes the dowager, e.g. The Dowager Lady Smith.
In the case of 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, but in this case without Christian name: "Lady" with the surname of the husband only, Sir John and Lady Smith. When a woman divorces a knight and he marries again, the new wife will be Lady Smith while the ex-wife becomes Jane, Lady Smith.
Female members of the Order of the Garter and Order of the Thistle also receive the prefix of "Lady"; here that title is prefixed to the given and family name of the lady, e.g. Lady Marion Fraser, LT, with the post nominal LG or LT respectively, and this is preserved if the lady marries.
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 hlǣfdigan "of the Lady".
The word is also used as a title of the Wicca goddess, The Lady.