Green shoe option is used in the context of initial public offering (IPO) in the stock market. It refers to option of allocating shares in excess of the shares which are included in the public issue. Green Shoe Company was the first one to issue such type of option and therefore it is called green shoe option.
Green shoe option is used in order to stabilize the price of stock when it gets listed, since company wants to sell shares to public it needs middle man which is underwriter in case of initial public offering. The underwriter can sell 15 percent more shares than originally planned. Underwriter usually sells those 15 percent shares to public.
Suppose when stock or share gets listed in stock exchange and trades below the issue price then underwrite can buy those 15 percent shares from the market, thereby stabilizing the price of stock and then there is no need for green shoe option. However if the stock price shoots up then it will create problem for underwriter as underwriter has short sold stock (since issuing 15 percent more than planned), then the underwriter will go for green shoe option where the company or promoter grants the underwriters the option to take shares or stocks from the company up to 15% than the original offering size.