C# is just one of the lanuages supported by the .NET Framework. The core of the functionality is provided by the framework and C# is used for consuming these classes offered by the Framework.
As for the .NET Framework, it offers capability to build various types of applications ranging from WebServices to Windows Services and from web applications to Windows based applications serving various domains.
If you want to get an idea from what has been C# used for in the real world then take a look at the casestudies here.
Regards,
Vikram