A special dividend is a payment made by a company to its shareholders, that the company declares to be separate from the typical recurring dividend cycle, if any, for the company.
Usually when a company raises the amount of its normal dividend, the investor expectation is that this marks a sustained increase. In the case of a special dividend, however, the company is signalling that this is a one-off payment. Therefore, special dividends do not markedly affect valuation or yield calculations, unless the amount is large -- in which case they do markedly affect valuation as they are a direct and large depletion of the assets of the company. Typically, special dividends are distributed if a company has exceptionally strong earnings that it wishes to distribute to shareholders, or if it is making changes to its financial structure, such as debt ratio.
A prominent example of a special dividend was the $3 dividend announced by Microsoft in 2004, to partially relieve its balance sheet of a large cash balance. A more recent example of a special dividend is the $1 dividend announced by SAIC (U.S. company) in 2013, just prior to it splitting off its solutions business into a new company named Leidos.
For special dividends, the ex-dividend date is set according to the size of the dividend in relation to the price of the security, and dividends or distributions of less than 25% are subject to the 'regular' rules for ex-dividend dates.
However, dividends or distributions of more than 25% are subject to 'special' rules for ex-dividend dates. The major difference here is that for these larger distributions or dividends, the ex-dividend date is set as the day after payment (with the day of payment being the "payment date").
For these larger 'special dividends', the ex-dividend date is generally one stock trading day after the dividend payment date. The dividend payment date occurs sometime after the dividend record date. The stock will trade on an ex-distribution basis (adjusted for the amount of the dividend paid) on the trading day after the dividend payment date, and thereafter.