Emacs provides a nice set of commands to copy a region in a buffer to another buffer or to write it to a file. In each case, these functions will prompt for the name of the file or buffer when called interactively. The functions are:
Despite its name, this function does not, strictly speaking append the region to a new buffer. Rather it inserts it in the new buffer at point.
This command replaces the text in the new buffer with the region from the current buffer.
Append the region onto the end of the file.
Write the region to the named file. When called from Elisp, this function has 4 optional arguments that control whether or not to append to the file, whether the file can already exist, and alternate naming.
These aren't commands that you'll use a lot but they are convenient for moving part of a buffer to another buffer or file.