Buying back shares become Treasury Stock.

They reduce the number of outstanding shares, fewer shares will effect the EPS calculation and if enough as a percent of the total outstanding shares are reacquired, then the pps may be adjusted in proportion.

The main reasons for acquiring shares are to improve the EPS, retire a specific number of shares and sometimes they are used to provide incentives to officers and employees in lieu of cash or salary adjustments.

Accounting wise, cash is reduced and in most cases a line in the equity section of the Balance Sheet is shown as Treasury stock, which is negative and reduces the total equity.

This is the simplest explanation, there are other more complexities than stated, and I believe there are quantity limits and other ramifications that escape me at the moment.

Hope this helps to clarify some of the discussion.