A named style is a collection of related style settings that have been placed in a file. The file, in turn, is added to a JCR content repository that is accessible to the Repository Service. When you are requesting a map, and you want the map to use a named style, you add a reference to the file that contains the named style in the XML request.
For example, to display a map overlay using an AreaStyle that is contained in a file named AreaStyleGreen and which has been added to a JCR repository under a directory named NamedStyles, your XML request would contain a line such as the following:
<v3:Style
xsi:type="v3:NamedStyle"
name="/NamedStyles/AreaStyleGreen"
xmlns:v3="http://www.mapinfo.com/midev/service/style/v1"/>