What's this C# "using" directive?

That's aliasing a typename to a shorter name. The same syntax can also be used for aliasing namespaces. See using directive.

(Updated in response to Richard)

It's an alias, from now on, the user can use StringFormat to refer to System.Drawing.StringFormat. It's useful if you don't want to use the whole namespace (in case of name clash issues for example).

source: using Directive article from MSDN

Perhaps a different, unrelated StringFormat is declared in another namespace like Acme.Stuff. If that were the case, this would cause confusion:

using System.Drawing; // Contains StringFormat type.
using Acme.Stuff;  // Contains another StringFormat type.

private void Foo()
{
    StringFormat myFormat = new StringFormat(); // which one to use?
}

Aliasing is with using on the StringFormat=System.Drawing.StringFormat clears up some of the confusion.