@a8 The company can either "retire" them or "hold" them, but the difference between them is largely meaningless. Either way, the shares don't circulate, don't earn dividends, don't count in EPS, etc. Nobody "gets" them.
Buy backs are supposed to increase the value of each share in the company, but of course that's all dependent on how the market perceives them. How much they increase stock value is likely too complicated for a short explanation here, and beyond what I know certainly.
The only real reason why companies do buy-backs instead of dividends is simply that a buy-back "should" increase the value of a share, and that's favorable from a tax perspective for investors, since in the US, capital gains has a more favorable tax status than dividends, which are taxed at ordinary income tax rates.