The purchase by a company of its own shares in the open market, usually based on the belief that the shares are undervalued and that buying them will provide a better investment return than using the cash for the underlying business of the company.  In theory the buy back will reduce the number of shares in the market and increase the value of the remaining ones.  This process is also known as a share repurchase.  It effectively returns to the shareholders the cash held in company reserves which already belongs to them.