Introduced to Europe via trade with Asia and in contrast to the very fitted costume typical for European men in the 18th century, the Banyan was a loose robe based on those worn in India, China and Japan. Popular for casual wear in the home, it was believed to assist in relaxing the body to allow exercise of the mind. As a consequence, intellectual men were often painted wearing a banyan, such as in James Thornhill's portrait of Isaac Newton c.1710.
This example is particularly fine; not only is the style inspired by exotic shapes, but the fabric itself is very high quality dragon silk, probably intended for use by the imperial court in China. The survival of both the waistcoat and robe together is extraordinary.
See 400 Years of Fashion, Victoria & Albert Museum; and Fashion: The Collection of the Kyoto Costume Museum, for brief discussions of the importance of the Banyan in 18th century style.