The practice of companies returning capital to their shareholders by buying in some of their own shares. Buybacks benefit shareholders by reducing their income tax bills. Share buybacks tend to raise the price of the remaining shares whereas distribution of the same amount in dividends tends to reduce it. This may benefit directors and other employees holding share options as part of their remuneration. The theoretical motivation for a buyback is that the deductibility of interest payments from profit before tax leads to a preference for debt finance over equity finance. It may be profitable for a firm to reduce its outstanding equity and finance new investment by borrowing.
Reference: Oxford Press Dictonary of Economics, 5th edt.