usually call it esmoquin. The smoking jacket is a formal evening suit tag to wear in evening parties and award ceremonies, cocktail parties and other social events. This kind of clothing is worn by men.
Smocking jacket got its name because it was a different garment that men wore to smok. It appeared in 1860. In Britain it became a popular outfitamong the middle and upper class. This garment became known worldwide and in a few weeks all men of themiddle and upper classes wore that.
The garment became more popular when the brand Hugo Boss was interested in the garment and they began to sell it in all Hugo Boss stores around the world.
Currently the smoking jacket is still used for evening events and in my opinion it's a suit that much stylized men.