Understanding SQL Server permissions
db_datawriter has no items in the permissions page because it doesn't have explicit object permissions as such. Rights are implied by the role.

MSDN for db_datawriter says


  Members of the db_datawriter fixed database role can add, delete, or change data in all user tables.


It has INSERT, UPDATE, DELETE on tables as per another MSDB page Permissions of Fixed Database Roles


  Granted: DELETE, INSERT, UPDATE


Finally, what does the DB engine say (SQL Server 2008 R2)?

EXEC sp_dbfixedrolepermission 'db_datawriter'

db_datawriter   DELETE permission on any object
db_datawriter   INSERT permission on any object
db_datawriter   UPDATE permission on any object


The MSDN pages for SQL Server 2008 are here (different page hierarchy)