A run is an arbitrary sequence of characters in an Office System Word 2003 document. In Visual Basic for Applications for Word, this would probably be called a Range. The run element, <r /> is documented here:

http://msdn.microsoft.com/library/en-us/
    WordXMLCDK/html/cdkweler_simpleFieldType_HV01114797.asp

The run property child element, <rPr /> , of the run element is designed to deal with the problem of "multiple formatting"---say, applying bold and italic to characters.