An odd-lot buyback occurs when a company offers to purchase shares of its stock back from people who hold less than 100 shares.
A popular method that companies use to buy back stocks is called a Dutch auction. Shareholders who are interested in participating in the auction indicate a price range within which they would be willing to sell their stocks back. The company will buy back the shares from the lowest tendered offers, all at the same price. The price is the highest of the accepted offers.
This type of offer makes it less expensive both for the company (due to the reduced cost of servicing these small shareholder accounts) and for the shareholders (because they do not have to pay brokerage fees to sell their shares). A buyback also can increase a stock's price-to-earnings ratio by decreasing the number of outstanding shares.
Some investors consider buybacks when evaluating a particular stock's potential. In the Kiplinger.com article "Winners Among Companies That Buy Back Stock" (March 2005), David Fried states that an odd lot buyback is "an enormous vote of confidence by those who know it best - the company's senior executives," and that "companies buy back stock when they are really undervalued or when there's something positive that's going to happen."
To go through the mechanics of a share buyback and what it means for investors, read our related article A Breakdown of Stock Buybacks.
This question was answered by Katie Adams.