What's a Waistcoat (or Vest) ?
A waistcoat (/ˈwɛskət/ or /ˈweɪstkoʊt/; colloquially called a weskit, derived from the French veste), or vest, is a sleeveless upper-body garment. It is usually worn over a dress shirt and necktie and below a coat as a part of most men's formal wear. It is also sported as the third piece in the traditional three-piece male lounge suit. Any given vest can be simple or ornate, or for leisure or luxury. Historically, the vest can be worn either in the place of or underneath a larger coat dependent upon the weather, wearer, and setting.
A waistcoat has a full vertical opening in the front, which fastens with buttons or snaps. Both single-breasted and double-breasted waistcoats exist, regardless of the formality of dress, but single-breasted ones are more common. In a three piece suit, the cloth used matches the jacket and trousers. Waistcoats can also have lapels or revers depending on the style.
Daytime formal wear and semi-formal wear commonly comprises a contrastingly coloured waistcoat, such as in buff or dove gray, still seen in morning dress and black lounge suit. For white tie and black tie, it is traditionally white and black, respectively.
The term waistcoat is used in the United Kingdom and many Commonwealth countries. The term vest is used widely in the United States and Canada, and is often worn as part of formal attire or as the third piece of a lounge suit in addition to a jacket and trousers. The term vest derives from the French language veste “jacket, sport coat", the term for a vest-waistcoat in French today being "gilet", the Italian language veste "robe, gown", and the Latin language vestis. The term vest in European countries refers to the A-shirt, a type of athletic vest. The Banyan, a garment of India, is commonly called a vest in Indian English.
Source : Vests Wikipedia