Normally Emacs uses the environment variable HOME (see HOME) to find .emacs; that's what ‘~’ means in a file name. If .emacs is not found inside ~/ (nor .emacs.el), Emacs looks for ~/.emacs.d/init.el (which, like ~/.emacs.el, can be byte-compiled).
However, if you run Emacs from a shell started by
tries to find your own .emacs, not that of the user you are
currently pretending to be. The idea is that you should get your own
editor customizations even if you are running as the super user.
More precisely, Emacs first determines which user's init file to use. It gets your user name from the environment variables LOGNAME and USER; if neither of those exists, it uses effective user-ID. If that user name matches the real user-ID, then Emacs uses HOME; otherwise, it looks up the home directory corresponding to that user name in the system's data base of users.