When companies accumulate excess cash and cast about for ways to use that cash, they have several options: increase dividends, pay down debt, do acquisitions, and engage in share buybacks. There are several solid reasons for engaging in share repurchases.
Buybacks are a tax-efficient way to return money to shareholders. As the company buys its shares back, the value of the shares outstanding will increase because each shareholderes shares now represent a larger piece of the pie. The shareholders won't owe taxes on the increase until they later sell their shares. Buybacks are also a way for management to signal to the market that the company's stock is undervalued and that the company expects solid performance ahead. Finally, when interest rates are low, paying down debt may not be a good option for all of that excess cash. Some companies like buybacks because of the EPS boost they get; profits are divided among fewer shares in calculating EPS resulting in higher earnings per share.
Here's another reason companies may engage in buybacks: as a company buys back its shares, the stock price increases and this provides back-door compensation to executives because their stock options are worth more. It would be possible, for example, for an aggressive buyback program to cause underwater options to become in-the-money options. The buyback will almost certainly cause the value of in-the-money options to increase.
When companies do share splits, they account for the split as they calculate options. For example, a company that does a 2-for-1 share split will convert employees' options to options for twice as many shares at half the price. If Bob has 100 options at $10 per share, after the 2-for-1 split he will have 200 options at $5 per share.
When companies engage in buybacks, there's no similar accounting adjustment with respect to stock options. So the increase in the stock price results in compensation to executives as the value of their stock options increases. Nice trick.