Rule 10b-18
  
Stock buybacks involve companies purchasing their own stock on the public market. The purpose is to support the stock price. The company takes shares off the market, lowering supply and thus providing a higher stock price.
Rule 10b-18 allows companies to do this. It wasn't always the case. Prior to the 1980s, companies couldn't buy shares off the open market like that (you could argue it smacks of price manipulation...and, originally, under the Securities Exchange Act of 1934, it fell under anti-fraud rules). But, in 1982, the rule was changed and buybacks were made legal.
Rule 10b-18 is the vehicle for the change. It gives companies so-called "safe harbor" to purchase shares on the open market, without running afoul of the anti-fraud laws. There are regulations the company has to follow...conditions within the rule that have to be met to get the safe harbor treatment. But within those stipulations, it's now completely legal.