Lisp code for Emacs editing commands is stored in files whose names conventionally end in .el. This ending tells Emacs to edit them in Emacs-Lisp mode (Section 25.6).
To execute a file of Emacs Lisp code, use M-x load-file. This command reads a file name using the minibuffer and then executes the contents of that file as Lisp code. It is not necessary to visit the file first; in any case, this command reads the file as found on disk, not text in an Emacs buffer.
Once a file of Lisp code is installed in the Emacs Lisp library directories, users can load it using M-x load-library. Programs can load it by calling load-library, or with load, a more primitive function that is similar but accepts some additional arguments.
M-x load-library differs from M-x load-file in that it searches a sequence of directories and tries three file names in each directory. Suppose your argument is lib; the three names are lib.elc, lib.el, and lastly just lib. If lib.elc exists, it is by convention the result of compiling lib.el; it is better to load the compiled file, since it will load and run faster.
If load-library finds that lib.el is newer than lib.elc file, it prints a warning, because it's likely that somebody made changes to the .el file and forgot to recompile it.
Because the argument to load-library is usually not in itself a valid file name, file name completion is not available. Indeed, when using this command, you usually do not know exactly what file name will be used.
The sequence of directories searched by M-x load-library is specified by the variable load-path, a list of strings that are directory names. The default value of the list contains the directory where the Lisp code for Emacs itself is stored. If you have libraries of your own, put them in a single directory and add that directory to load-path. nil in this list stands for the current default directory, but it is probably not a good idea to put nil in the list. If you find yourself wishing that nil were in the list, most likely what you really want to do is use M-x load-file this once.
Often you do not have to give any command to load a library, because the commands defined in the library are set up to autoload that library. Trying to run any of those commands calls load to load the library; this replaces the autoload definitions with the real ones from the library.
Emacs Lisp code can be compiled into byte-code which loads faster, takes up less space when loaded, and executes faster. . By convention, the compiled code for a library goes in a separate file whose name consists of the library source file with c appended. Thus, the compiled code for foo.el goes in foo.elc. That's why load-library searches for .elc files first.
By default, Emacs refuses to load compiled Lisp files which were compiled with XEmacs, a modified versions of Emacs--they can cause Emacs to crash. Set the variable load-dangerous-libraries to t if you want to try loading them.