What does ifstream::rdbuf() actually do?

iostream classes are just wrappers around I/O buffers. The iostream itself doesn't do a whole lot… mainly, it the provides operator>> formatting operators. The buffer is provided by an object derived from basic_streambuf, which you can get and set using rdbuf().

basic_streambuf is an abstract base with a number of virtual functions which are overridden to provide a uniform interface for reading/writing files, strings, etc. The function basic_ostream<…>::operator<<( basic_streambuf<…> ) is defined to keep reading through the buffer until the underlying data source is exhausted.

iostream is a terrible mess, though.

Yes, it's specified in the standard and it's actually quite simple. rdbuf() just returns a pointer to the underlying basic_streambuf object for the given [io]stream object.

basic_ostream<...> has an overload for operator<< for a pointer to basic_streambuf<...> which writes out the contents of the basic_streambuf<...>.