Various programs such as mail can invoke your choice of editor to edit a particular piece of text, such as a message that you are sending. By convention, most of these programs use the environment variable EDITOR to specify which editor to run. If you set EDITOR to emacs, they invoke Emacs--but in an inconvenient fashion, by starting a new, separate Emacs process. This is inconvenient because it takes time and because the new Emacs process doesn't share the buffers in the existing Emacs process.
You can arrange to use your existing Emacs process as the editor for programs like mail by using the Emacs client and Emacs server programs. Here is how.
First, the preparation. Within Emacs, call the function server-start. (Your .emacs file can do this automatically if you add the expression (server-start) to it.) Then, outside Emacs, set the EDITOR environment variable to emacsclient. (Note that some programs use a different environment variable; for example, to make TeX use emacsclient, you should set the TEXEDIT environment variable to emacsclient +%d %s.)
Then, whenever any program invokes your specified EDITOR program, the effect is to send a message to your principal Emacs telling it to visit a file. (That's what the program emacsclient does.) Emacs displays the buffer immediately and you can immediately begin editing it.
When you've finished editing that buffer, type C-x # (server-edit). This saves the file and sends a message back to the emacsclient program telling it to exit. The programs that use EDITOR wait for the "editor" (actually, emacsclient) to exit. C-x # also checks for other pending external requests to edit various files, and selects the next such file.
You can switch to a server buffer manually if you wish; you don't have to arrive at it with C-x #. But C-x # is the only way to say that you are "finished" with one.
Finishing with a server buffer also kills the buffer, unless it already existed in the Emacs session before the server asked to create it. However, if you set server-kill-new-buffers to nil, then a different criterion is used: finishing with a server buffer kills it if the file name matches the regular expression server-temp-file-regexp. This is set up to distinguish certain "temporary" files.
If you set the variable server-window to a window or a frame, C-x # displays the server buffer in that window or in that frame.
While mail or another application is waiting for emacsclient to finish, emacsclient does not read terminal input. So the terminal that mail was using is effectively blocked for the duration. In order to edit with your principal Emacs, you need to be able to use it without using that terminal. There are three ways to do this:
Using a window system, run mail and the principal Emacs in two separate windows. While mail is waiting for emacsclient, the window where it was running is blocked, but you can use Emacs by switching windows.
Using virtual terminals, run mail in one virtual terminal and run Emacs in another.
Use Shell mode or Term mode in Emacs to run the other program such as mail; then, emacsclient blocks only the subshell under Emacs, and you can still use Emacs to edit the file.
If you run emacsclient with the option -no-wait, it returns immediately without waiting for you to "finish" the buffer in Emacs. Note that server buffers created in this way are not killed automatically when you finish with them.