Dame is an honorific title and the feminine form of address for the honour of knighthood in the British honours system and the systems of several other Commonwealth countries, such as Australia, and New Zealand (with the masculine form of address being "Sir"). The word "damehood" is rarely used, but it is used on the official British Monarchy website as being the correct term.
A woman appointed to the grades of Dame Commander or Dame Grand Cross of the Most Honourable Order of the Bath, the Most Distinguished Order of Saint Michael and Saint George, the Royal Victorian Order, or the Most Excellent Order of the British Empire becomes a dame. Since there is no female equivalent to a Knight Bachelor, women are always appointed to an order of chivalry. Women who are appointed to the Most Noble Order of the Garter or the Most Ancient and Most Noble Order of the Thistle are given the title of "Lady" rather than "Dame".
The Order of the Ermine, founded by John V, Duke of Brittany in 1381, was the first order of chivalry to accept women; however, female knights existed for centuries in many places in the world prior to this. Like their male counterparts, they were distinguished by the flying of coloured banners and generally bore a coat of arms.