In Calc this option is only available for cell styles. You can use this option to link styles. If you link styles, then when you change the base style (for example, by changing the font from Times to Helvetica), all the linked styles will change as well. Sometimes this is exactly what you want; other times you do not want the changes to apply to all the linked styles. It pays to plan ahead.
For example, you can make a new style called red, in which the only change you want to make is for the cell text to be red. In order to make sure that the rest of the text characteristics are the same as the default style, you can link red with default. Then, any changes you make to default will be automatically applied to red.