AFIEDT.BUF is the SQL*Plus default edit save file. When you issue the command "ed" or "edit" without arguments, the last SQL or PL/SQL command will be saved to a file called AFIEDT.BUF and opened in the default editor.
In the prehistoric days when SQL*Plus was called UFI (User Friendly Interface) this file was named "ufiedt.buf", short for UFI editing buffer. When new features were added to UFI, it was the initially named Advanced UFI and the filename was changed to "aufiedt.buf" and then to "afiedt.buf". They presumably needed to keep the name short for compatibility with some of the odd operating systems that Oracle supported in those days. The name "Advanced UFI" was never used officially, as the name was changed to SQL*Plus before this version was released.
You can overwrite the default edit save file's name like this:
SET EDITFILE "afiedt.buf"