A special dividend is a dividend that is stated to be a special dividend when it is declared. The main reason for declaring a dividend special is to make it clear that it is a one-off. This is a signal to investors that it is not part of a sustainable increase in dividends.
Usually, when a company raises its dividend, the market takes this as signalling that the company will keep paying dividends at the new higher level. It may also signal a change in the company's policy regarding dividends.
Labelling a dividend "special" makes it clear that the company does not wish to signal this.
It is quite usual for a company to pay a special dividend and increase its normal dividend as well. In this case the increase to the normal dividend is a signal and can be taken as indicating the company's current dividend policy. The (usually much bigger) increase due to the special dividend is not.
For this reason the special dividend should not be included in yield calculations and has only a a limited effect on valuation.
Special dividends are most often used to return capital to shareholders.